\documentclass[12pt]{article}
\usepackage{ed,amssymb}


% Optionally set the location for graphics files on the Maple T.A. system.
%\setImageBase{...}

%\begin{question}{question type}
%...
%\end{question}


\begin{document}

\begin{topic}{Basic properties of functions}

%%% Range, ax+b %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{question}{Multiple Choice}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a=range(1,12,1);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$fgv=maple("($a)*x+($b)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\choice*{$\mathbb{R}=\,]-\infty,\infty[\,$}
\choice{$]-\infty,\var{a}]$}
\choice{$[\var{a},\infty[\,$}
\choice{$[0,\infty[\,$}
\choice{$\,]-\infty,0]$}
\choice{$\,]-\infty,\var{a}]$}
\choice{$[-\var{a},\infty[\,$}
\choice{$[0,\var{a}]$}
\choice{$[-\var{a},0]$}
\choice{$[-\var{a},\var{a}]$}
\end{question}



%%% Range, ax^2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{question}{Multiple Choice}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("($a)*x^2");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\choice{$\mathbb{R}=\,]-\infty,\infty[\,$}
\choice{$]-\infty,\var{a}]$}
\choice{$[\var{a},\infty[\,$}
\choice*{$[0,\infty[\,$}
\choice{$\,]-\infty,0]$}
\choice{$\,]-\infty,\var{a}]$}
\choice{$[-\var{a},\infty[\,$}
\choice{$[0,\var{a}]$}
\choice{$[-\var{a},0]$}
\choice{$[-\var{a},\var{a}]$}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("(-($a))*x^2");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\choice{$\mathbb{R}=\,]-\infty,\infty[\,$}
\choice{$]-\infty,\var{a}]$}
\choice{$[\var{a},\infty[\,$}
\choice{$[0,\infty[\,$}
\choice*{$\,]-\infty,0]$}
\choice{$\,]-\infty,\var{a}]$}
\choice{$[-\var{a},\infty[\,$}
\choice{$[0,\var{a}]$}
\choice{$[-\var{a},0]$}
\choice{$[-\var{a},\var{a}]$}
\end{question}




%%% Range, sqrt(x) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{question}{Multiple Choice}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("sqrt(($a)*x)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\choice{$\mathbb{R}=\,]-\infty,\infty[\,$}
\choice{$]-\infty,\var{a}]$}
\choice{$[\var{a},\infty[\,$}
\choice*{$[0,\infty[\,$}
\choice{$\,]-\infty,0]$}
\choice{$\,]-\infty,\var{a}]$}
\choice{$[-\var{a},\infty[\,$}
\choice{$[0,\var{a}]$}
\choice{$[-\var{a},0]$}
\choice{$[-\var{a},\var{a}]$}
\end{question}



\begin{question}{Multiple Choice}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("($a)*sqrt(x)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\choice{$\mathbb{R}=\,]-\infty,\infty[\,$}
\choice{$]-\infty,\var{a}]$}
\choice{$[\var{a},\infty[\,$}
\choice*{$[0,\infty[\,$}
\choice{$\,]-\infty,0]$}
\choice{$\,]-\infty,\var{a}]$}
\choice{$[-\var{a},\infty[\,$}
\choice{$[0,\var{a}]$}
\choice{$[-\var{a},0]$}
\choice{$[-\var{a},\var{a}]$}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,-1,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("($a)*sqrt(x)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\choice{$\mathbb{R}=\,]-\infty,\infty[\,$}
%\choice{$]-\infty,\var{a}]$}
\choice{$[\var{a},\infty[\,$}
\choice{$[0,\infty[\,$}
\choice*{$\,]-\infty,0]$}
\choice{$\,]-\infty,\var{a}]$}
\choice{$[\var{a},\infty[\,$}
%\choice{$[0,\var{a}]$}
\choice{$[\var{a},0]$}
%\choice{$[-\var{a},\var{a}]$}
\end{question}




\begin{question}{Multiple Choice}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$fgv=maple("($a)*sqrt(x)+($b)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\choice{$\mathbb{R}=\,]-\infty,\infty[\,$}
\choice{$]-\infty,\var{b}]$}
\choice*{$[\var{b},\infty[\,$}
\choice{$[0,\infty[\,$}
\choice{$\,]-\infty,0]$}
\choice{$\,]-\infty,\var{b}]$}
\choice{$[-\var{a},\infty[\,$}
\choice{$[0,\var{a}]$}
\choice{$[-\var{a},0]$}
\choice{$[-\var{a},\var{a}]$}
\end{question}



\begin{question}{Multiple Choice}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,-1,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(1,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$fgv=maple("($a)*sqrt(x)+($b)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\choice{$\mathbb{R}=\,]-\infty,\infty[\,$}
\choice{$]-\infty,\var{b}]$}
\choice{$[\var{b},\infty[\,$}
\choice{$[0,\infty[\,$}
\choice{$\,]-\infty,0]$}
\choice*{$\,]-\infty,\var{b}]$}
\choice{$[-\var{b},\infty[\,$}
%\choice{$[0,\var{a}]$}
\choice{$[\var{a},0]$}
%\choice{$[-\var{a},\var{a}]$}
\choice{$[\var{a},\infty[\,$}
\end{question}






%%% Range, cos(), sin(), %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("cos(($a)*x)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[-2\Pi,2\Pi]\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("cos(($a)*x)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("cos(($a)*x)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}



\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("sin(($a)*x)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[-2\Pi,2\Pi]\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("sin(($a)*x)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("sin(($a)*x)");
$c=maple("[-1,1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}



%%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%%
\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
}
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("($a)*cos(x)");
$c=maple("[-($a),($a)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[-2\Pi,2\Pi]\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("($a)*cos(x)");
$c=maple("[-($a),($a)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("($a)*cos(x)");
$c=maple("[-($a),($a)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
}
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("($a)*sin(x)");
$c=maple("[-($a),($a)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[-2\Pi,2\Pi]\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("($a)*sin(x)");
$c=maple("[-($a),($a)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("($a)*sin(x)");
$c=maple("[-($a),($a)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}






%%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%%
\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
}
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("cos(x)+($a)");
$c=maple("[($a)-1,($a)+1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[-2\Pi,2\Pi]\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("cos(x)+($a)");
$c=maple("[($a)-1,($a)+1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("cos(x)+($a)");
$c=maple("[($a)-1,($a)+1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}





\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("sin(x)+($a)");
$c=maple("[($a)-1,($a)+1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[-2\Pi,2\Pi]\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
}
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("sin(x)+($a)");
$c=maple("[($a)-1,($a)+1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$fgv=maple("sin(x)+($a)");
$c=maple("[($a)-1,($a)+1]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}





%%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%%
\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$fgv=maple("($a)*cos(($b)*x)+($d)");
$c=maple("[($d)-($a),($a)+($d)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[-2\Pi,2\Pi]\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$fgv=maple("($a)*cos(($b)*x)+($d)");
$c=maple("[($d)-($a),($a)+($d)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$fgv=maple("($a)*cos(($b)*x)+($d)");
$c=maple("[($d)-($a),($a)+($d)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}





\begin{question}{Maple}
\qutext{
Determine the range of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
Give your answer in one of the forms
$[a,b]$, $[a,b\,[\,$,  $\,]\,a,b]$, $\,]\,a,b[\,$,
$[a,infinity\,[\,$, $]\,-infinity,b]$,
$\,]\,a,infinity\,[\,$, $]\,-infinity,b\,[\,$
or $\,]\,-infinity,infinity\,[\,$.
 }
\code{
$a0=range(1,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$fgv=maple("($a)*sin(($b)*x)+($d)");
$c=maple("[($d)-($a),($a)+($d)]");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}





%%% $x$-intercept %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{question}{Maple}
\qutext{
Determine the $x$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-6,6,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-5,5,1);
$c=if(eq($c0,0),$c0+1,$c0);
$fgv=maple("($a)*x-($a)*($c)");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the $x$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$fgv=maple("(x-($c))^3");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}




%%% $y$-intercept %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv=maple("($a)*x+($c)");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b=range(-12,12,1);
$c=range(-12,12,1);
$fgv=maple("($a)*x^2+($b)*x+($c)");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$fgv=maple("(x+($c))^2");
$ANSWER=maple("($c)^2");
}
\maple{($c)^2}
\end{question}



\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b=range(-12,12,1);
$d=range(-12,12,1);
$c=range(-12,12,1);
$fgv=maple("($a)*x^3+($b)*x^2+($d)*x+($c)");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$c0=range(-5,5,1);
$c=if(eq($c0,0),$c0+1,$c0);
$fgv=maple("(x+($c))^3");
$ANSWER=maple("($c)^3");
}
\maple{($c)^3}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv=maple("($a)*sqrt(x)+($c)");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv=maple("($a)*sin(x)+($c)");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv=maple("($a)*cos(x)+($c)");
$ANSWER=maple("($a)+($c)");
}
\maple{($a)+($c)}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$b0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b=if(eq($b0,0),$b0+1,$b0);
$c=range(-12,12,1);
$fgv=maple("($a)*cos(x)+($b)*sin(x)+($c)");
$ANSWER=maple("($a)+($c)");
}
\maple{($a)+($c)}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv=maple("($a)*(sin(x))^2+($c)");
$ANSWER=maple("$c");
}
\maple{$c}
\end{question}

\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv=maple("($a)*(cos(x))^2+($c)");
$ANSWER=maple("($a)+($c)");
}
\maple{($a)+($c)}
\end{question}


\begin{question}{Maple}
\qutext{
Determine the $y$-intercept of the graph of the function
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\var{fgv}$.
}
\code{
$a0=range(-12,12,1);
$b0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b=if(eq($b0,0),$b0+1,$b0);
$c=range(-12,12,1);
$fgv=maple("($a)*(cos(x))^2+($b)*(sin(x))^2+($c)");
$ANSWER=maple("($a)+($c)");
}
\maple{($a)+($c)}
\end{question}

\end{topic}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{topic}{Injectivity, surjectivity, bijectivity and invertibility of functions}


%%% Injectivity %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=x^3$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\cos(x)$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=x^2$}
\end{question}


%%% %%%
\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgv2}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgvs}$}
\end{question}


%%% %%% %%%
%%% %%%
\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$p=range(1,12,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgv5=maple("($p)*x^2");
}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to[0,\infty[\,$,    $f(x)=\var{fgv5}$}

\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=x^2$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvs}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=\var{fgv5}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$n=range(-12,1,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
$fgv6=maple("($n)*x^2");
}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv2}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice*{$f:[0,\infty[\,\to\,]-\infty,0]$,    $f(x)=\var{fgv6}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are injective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$n=range(-12,1,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
$fgv6=maple("($n)*x^2");
}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv2}$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to\,]-\infty,0]$,    $f(x)=\var{fgv6}$}
\end{question}



%%% Surjectivity %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,  $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,  $f(x)=x^3$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=x^2$}
\end{question}




\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\cos(x)$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}




\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=x^2$}
\end{question}




%%% %%%
\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgv2}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgvs}$}
\end{question}



%%% %%% %%%
%%% %%%
\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$p=range(1,12,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgv5=maple("($p)*x^2");
}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice*{$f:\mathbb{R}\to[0,\infty[\,$,    $f(x)=\var{fgv5}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=x^2$}
\end{question}

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvs}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=\var{fgv5}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$n=range(-12,1,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
$fgv6=maple("($n)*x^2");
}
\choice*{$f:\mathbb{R},\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv2}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice*{$f:[0,\infty[\,\to\,]-\infty,0]$,    $f(x)=\var{fgv6}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are surjective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$n=range(-12,1,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
$fgv6=maple("($n)*x^2");
}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv2}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice*{$f:\mathbb{R}\to\,]-\infty,0]$,    $f(x)=\var{fgv6}$}
\end{question}


%%% Bijectivity %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,  $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,  $f(x)=x^3$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=x^2$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\cos(x)$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}



\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=x^2$}
\end{question}



%%% %%%
\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgv2}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgvs}$}
\end{question}



%%% %%% %%%
%%% %%%
\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$p=range(1,12,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgv5=maple("($p)*x^2");
}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to[0,\infty[\,$,    $f(x)=\var{fgv5}$}
\end{question}

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=x^2$}
\end{question}

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvs}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=\var{fgv5}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$n=range(-12,1,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
$fgv6=maple("($n)*x^2");
}
\choice*{$f:\mathbb{R},\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv2}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice*{$f:[0,\infty[\,\to\,]-\infty,0]$,    $f(x)=\var{fgv6}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are bijective.
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$n=range(-12,1,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
$fgv6=maple("($n)*x^2");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv2}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to\,]-\infty,0]$,    $f(x)=\var{fgv6}$}
\end{question}



%%% Invertibility %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=x^3$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\cos(x)$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=x^2$}
\end{question}



\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$b=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$c=range(-12,12,1);
$fgv1=maple("($a)*x+($b)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\sin(x)$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=x^2$}
\end{question}





%%% %%%
\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgv2}$}
\end{question}

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,    $f(x)=\var{fgvs}$}
\end{question}



%%% %%% %%%
%%% %%%
\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to[0,\infty[\,$,    $f(x)=\var{fgv2}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=x^2$}
\end{question}

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice*{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv3}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvs}$}
\choice*{$f:[0,\infty[\,\to[0,\infty[\,$,    $f(x)=\var{fgv5}$}
\end{question}

\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$n=range(-12,1,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
$fgv6=maple("($n)*x^2");
}
\choice*{$f:\mathbb{R},\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv2}$}
\choice{$f:[0,\infty[\,\to\mathbb{R}$,    $f(x)=\var{fgvc}$}
\choice*{$f:[0,\infty[\,\to\,]-\infty,0]$,    $f(x)=\var{fgv6}$}
\end{question}


\begin{question}{Multiple Selection}
\qutext{
Determine which of the following functions are invertible (on their entire domain).
}
\code{
$a0=range(-12,12,1);
$a=if(eq($a0,0),$a0+1,$a0);
$b0=range(-12,12,1);
$b=if(eq($b0,0),$b0+1,$b0);
$c0=range(-12,12,1);
$c=if(eq($c0,0),$c0+1,$c0);
$d0=range(-12,12,1);
$d=if(eq($d0,0),$d0+1,$d0);
$e0=range(-12,12,1);
$e=if(eq($e0,0),$e0+1,$e0);
$f0=range(-12,12,1);
$f=if(eq($f0,0),$f0+1,$f0);
$g0=range(-12,12,1);
$g=if(eq($g0,0),$g0+1,$g0);
$h0=range(-12,12,1);
$h=if(eq($h0,0),$h0+1,$h0);
$i0=range(-12,12,1);
$i=if(eq($i0,0),$i0+1,$i0);
$j0=range(-12,12,1);
$j=if(eq($j0,0),$j0+1,$j0);
$k0=range(-12,12,1);
$k=if(eq($k0,0),$k0+1,$k0);
$sa0=range(-12,12,1);
$sa=if(eq($sa0,0),$sa0+1,$sa0);
$sb0=range(-12,12,1);
$sb=if(eq($sb0,0),$sb0+1,$sb0);
$sc0=range(-12,12,1);
$sc=if(eq($sc0,0),$sc0+1,$sc0);
$ca0=range(-12,12,1);
$ca=if(eq($ca0,0),$ca0+1,$ca0);
$cb0=range(-12,12,1);
$cb=if(eq($cb0,0),$cb0+1,$cb0);
$cc0=range(-12,12,1);
$cc=if(eq($cc0,0),$cc0+1,$cc0);
$p=range(1,12,1);
$n=range(-12,1,1);
$fgv1=maple("($a)*x+($b)");
$fgv2=maple("($c)*x^2+($d)*x+($e)");
$fgv3=maple("($f)*x^3+($g)*x^2+($h)*x+($i)");
$fgv4=maple("($j)*sqrt(x)+($k)");
$fgvc=maple("($ca)*cos(($cb)*x)+($cc)");
$fgvs=maple("($sa)*sin(($sb)*x)+($sc)");
$fgv5=maple("($p)*x^2");
$fgv6=maple("($n)*x^2");
}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$,   $f(x)=\var{fgv1}$}
\choice{$f:\mathbb{R}\to\mathbb{R}$,   $f(x)=\var{fgv2}$}
\choice*{$f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\var{fgv4}$}
\choice{$f:\mathbb{R}\to\,]-\infty,0]$,    $f(x)=\var{fgv6}$}
\end{question}

\end{topic}





\begin{topic}{Shifting and scaling the graph of a function}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function and let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=f(x)+c$ from the graph of $f$?
}
\choice*{Shifting the graph of $f$ upwards by $c$ units.}
\choice{Shifting the graph of $f$ downwards by $c$ units.}
\choice{Shifting the graph of $f$ to the left by $c$ units.}
\choice{Shifting the graph of $f$ to the right by $c$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $c$.}
\choice{Stretching the graph of $f$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function and let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=f(x)-c$ from the graph of $f$?
}
\choice{Shifting the graph of $f$ upwards by $c$ units.}
\choice*{Shifting the graph of $f$ downwards by $c$ units.}
\choice{Shifting the graph of $f$ to the left by $c$ units.}
\choice{Shifting the graph of $f$ to the right by $c$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $c$.}
\choice{Stretching the graph of $f$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function and let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=f(x+c)$ from the graph of $f$?
}
\choice{Shifting the graph of $f$ upwards by $c$ units.}
\choice{Shifting the graph of $f$ downwards by $c$ units.}
\choice*{Shifting the graph of $f$ to the left by $c$ units.}
\choice{Shifting the graph of $f$ to the right by $c$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $c$.}
\choice{Stretching the graph of $f$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function and let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=f(x-c)$ from the graph of $f$?
}
\choice{Shifting the graph of $f$ upwards by $c$ units.}
\choice{Shifting the graph of $f$ downwards by $c$ units.}
\choice{Shifting the graph of $f$ to the left by $c$ units.}
\choice*{Shifting the graph of $f$ to the right by $c$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $c$.}
\choice{Stretching the graph of $f$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=f(-x)$ from the graph of $f$?
}
\choice{Shifting the graph of $f$ upwards.}
\choice{Shifting the graph of $f$ downwards.}
\choice{Shifting the graph of $f$ to the left.}
\choice{Shifting the graph of $f$ to the right.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice*{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically.}
\choice{Stretching the graph of $f$ vertically
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-f(x)$ from the graph of $f$?
}
\choice{Shifting the graph of $f$ upwards.}
\choice{Shifting the graph of $f$ downwards.}
\choice{Shifting the graph of $f$ to the left.}
\choice{Shifting the graph of $f$ to the right.}
\choice*{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically.}
\choice{Stretching the graph of $f$ vertically
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function and let $c>1$ be a  real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=cf(x)$ from the graph of $f$?
}
\choice{Shifting the graph of $f$ upwards by $c$ units.}
\choice{Shifting the graph of $f$ downwards by $c$ units.}
\choice{Shifting the graph of $f$ to the left by $c$ units.}
\choice{Shifting the graph of $f$ to the right by $c$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice*{Stretching the graph of $f$ vertically by the factor $c$.}
\choice{Stretching the graph of $f$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function and let $c>1$ be a  real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-cf(x)$ from the graph of $f$?
}
\choice{Shifting the graph of $f$ upwards by $c$ units.}
\choice{Shifting the graph of $f$ downwards by $c$ units.}
\choice{Shifting the graph of $f$ to the left by $c$ units.}
\choice{Shifting the graph of $f$ to the right by $c$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $c$.}
\choice*{Stretching the graph of $f$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=f(x)+\var{c}$ from the graph of $f$?
}
\code{
$c=range(1,20,1);
}
\choice*{Shifting the graph of $f$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=f(x)-\var{c}$ from the graph of $f$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $f$ upwards by $\var{c}$ units.}
\choice*{Shifting the graph of $f$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=f(x+\var{c})$ from the graph of $f$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $f$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ downwards by $\var{c}$ units.}
\choice*{Shifting the graph of $f$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=f(x-\var{c})$ from the graph of $f$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $f$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the left by $\var{c}$ units.}
\choice*{Shifting the graph of $f$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\var{c}f(x)$ from the graph of $f$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $f$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice*{Stretching the graph of $f$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $f:\mathbb{R}\to\mathbb{R}$ be a function.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-\var{c}f(x)$ from the graph of $f$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $f$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $f$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $f$ about the $x$-axis.}
\choice{Reflecting the graph of $f$ about the $y$-axis.}
\choice{Stretching the graph of $f$ vertically by the factor $\var{c}$.}
\choice*{Stretching the graph of $f$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:[0,\infty[\,\to\mathbb{R}$, $g(x)=\sqrt{x}+\var{c}$,
from the graph of $f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$?
}
\code{
$c=range(1,20,1);
}
\choice*{Shifting the graph of $\sqrt{x}$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $x$-axis.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $y$-axis.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:[0,\infty[\,\to\mathbb{R}$, $g(x)=\sqrt{x}-\var{c}$,
from the graph of $f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $\sqrt{x}$ upwards by $\var{c}$ units.}
\choice*{Shifting the graph of $\sqrt{x}$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $x$-axis.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $y$-axis.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$
and reflecting the result about the $\sqrt{x}$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g(x)=\sqrt{x+\var{c}}$,
from the graph of $f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $\sqrt{x}$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ downwards by $\var{c}$ units.}
\choice*{Shifting the graph of $\sqrt{x}$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $x$-axis.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $y$-axis.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g(x)=\sqrt{x-\var{c}}$,
from the graph of $f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $\sqrt{x}$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the left by $\var{c}$ units.}
\choice*{Shifting the graph of $\sqrt{x}$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $x$-axis.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $y$-axis.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:[0,\infty[\,\to\mathbb{R}$, $g(x)=\var{c}\sqrt{x}$,
from the graph of $f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $\sqrt{x}$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $x$-axis.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $y$-axis.}
\choice*{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:[0,\infty[\,\to\mathbb{R}$, $g(x)=-\sqrt{x}$,
from the graph of $f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$?
}
\choice{Shifting the graph of $\sqrt{x}$ upwards.}
\choice{Shifting the graph of $\sqrt{x}$ downwards.}
\choice{Shifting the graph of $\sqrt{x}$ to the left.}
\choice{Shifting the graph of $\sqrt{x}$ to the right.}
\choice*{Reflecting the graph of $\sqrt{x}$ about the $x$-axis.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $y$-axis.}
\choice{Stretching the graph of $\sqrt{x}$ vertically.}
\choice{Stretching the graph of $\sqrt{x}$ vertically
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:[0,\infty[\,\to\mathbb{R}$, $g(x)=-\var{c}\sqrt{x}$,
from the graph of $f:[0,\infty[\,\to\mathbb{R}$, $f(x)=\sqrt{x}$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $\sqrt{x}$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sqrt{x}$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $x$-axis.}
\choice{Reflecting the graph of $\sqrt{x}$ about the $y$-axis.}
\choice{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$.}
\choice*{Stretching the graph of $\sqrt{x}$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g(x)=(x-\var{c})^3$,
from the graph of $f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^3$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $x^3$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^3$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^3$ to the left by $\var{c}$ units.}
\choice*{Shifting the graph of $x^3$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $x^3$ about the $x$-axis.}
\choice{Reflecting the graph of $x^3$ about the $y$-axis.}
\choice{Stretching the graph of $x^3$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $x^3$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\end{topic}


\begin{topic}{Transformations of quadratic functions}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=x^2+c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\choice*{Shifting the graph of $x^2$ upwards by $c$ units.}
\choice{Shifting the graph of $x^2$ downwards by $c$ units.}
\choice{Shifting the graph of $x^2$ to the left by $c$ units.}
\choice{Shifting the graph of $x^2$ to the right by $c$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=x^2-c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\choice{Shifting the graph of $x^2$ upwards by $c$ units.}
\choice*{Shifting the graph of $x^2$ downwards by $c$ units.}
\choice{Shifting the graph of $x^2$ to the left by $c$ units.}
\choice{Shifting the graph of $x^2$ to the right by $c$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=(x+c)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\choice{Shifting the graph of $x^2$ upwards by $c$ units.}
\choice{Shifting the graph of $x^2$ downwards by $c$ units.}
\choice*{Shifting the graph of $x^2$ to the left by $c$ units.}
\choice{Shifting the graph of $x^2$ to the right by $c$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=(x-c)^2$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\choice{Shifting the graph of $x^2$ upwards by $c$ units.}
\choice{Shifting the graph of $x^2$ downwards by $c$ units.}
\choice{Shifting the graph of $x^2$ to the left by $c$ units.}
\choice*{Shifting the graph of $x^2$ to the right by $c$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=cx^2$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\choice{Shifting the graph of $x^2$ upwards by $c$ units.}
\choice{Shifting the graph of $x^2$ downwards by $c$ units.}
\choice{Shifting the graph of $x^2$ to the left by $c$ units.}
\choice{Shifting the graph of $x^2$ to the right by $c$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice*{Stretching the graph of $x^2$ vertically by the factor $c$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-cx^2$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\choice{Shifting the graph of $x^2$ upwards by $c$ units.}
\choice{Shifting the graph of $x^2$ downwards by $c$ units.}
\choice{Shifting the graph of $x^2$ to the left by $c$ units.}
\choice{Shifting the graph of $x^2$ to the right by $c$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $c$.}
\choice*{Stretching the graph of $x^2$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=x^2+\var{c}$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\code{
$c=range(1,20,1);
}
\choice*{Shifting the graph of $x^2$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=x^2-\var{c}$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $x^2$ upwards by $\var{c}$ units.}
\choice*{Shifting the graph of $x^2$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=(x+\var{c})^2$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $x^2$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ downwards by $\var{c}$ units.}
\choice*{Shifting the graph of $x^2$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=(x-\var{c})^2$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $x^2$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the left by $\var{c}$ units.}
\choice*{Shifting the graph of $x^2$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\var{c}x^2$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $x^2$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice*{Stretching the graph of $x^2$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-x^2$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\choice{Shifting the graph of $x^2$ upwards.}
\choice{Shifting the graph of $x^2$ downwards.}
\choice{Shifting the graph of $x^2$ to the left.}
\choice{Shifting the graph of $x^2$ to the right.}
\choice*{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically.}
\choice{Stretching the graph of $x^2$ vertically
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-\var{c}x^2$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=x^2$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $x^2$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $x^2$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $x^2$ about the $x$-axis.}
\choice{Reflecting the graph of $x^2$ about the $y$-axis.}
\choice{Stretching the graph of $x^2$ vertically by the factor $\var{c}$.}
\choice*{Stretching the graph of $x^2$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}
\end{topic}




\begin{topic}{Transformations of trigonometric functions}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)+c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)$?
}
\choice*{Shifting the graph of $\cos(x)$ upwards by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ downwards by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ to the left by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $c$.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)-c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)$?
}
\choice{Shifting the graph of $\cos(x)$ upwards by $c$ units.}
\choice*{Shifting the graph of $\cos(x)$ downwards by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ to the left by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $c$.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x+c)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)$?
}
\choice{Shifting the graph of $\cos(x)$ upwards by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ downwards by $c$ units.}
\choice*{Shifting the graph of $\cos(x)$ to the left by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $c$.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x-c)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)$?
}
\choice{Shifting the graph of $\cos(x)$ upwards by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ downwards by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ to the left by $c$ units.}
\choice*{Shifting the graph of $\cos(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $c$.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)+c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)$?
}
\choice{Shifting the graph of $\cos(x)$ upwards.}
\choice{Shifting the graph of $\cos(x)$ downwards.}
\choice{Shifting the graph of $\cos(x)$ to the left.}
\choice{Shifting the graph of $\cos(x)$ to the right.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice*{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically.}
\choice{Stretching the graph of $\cos(x)$ vertically
and reflecting the result about the $\cos(x)$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)+c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=-c\cos(x)$?
}
\choice{Shifting the graph of $\cos(x)$ upwards by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ downwards by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ to the left by $c$ units.}
\choice{Shifting the graph of $\cos(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $c$.}
\choice*{Stretching the graph of $\cos(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)+\var{c}$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\cos(x)$?
}
\code{
$c=range(1,20,1);
}
\choice*{Shifting the graph of $\cos(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x)-\var{c}$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\cos(x)$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $\cos(x)$ upwards by $\var{c}$ units.}
\choice*{Shifting the graph of $\cos(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\cos(x+\var{c})$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\cos(x)$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $\cos(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ downwards by $\var{c}$ units.}
\choice*{Shifting the graph of $\cos(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=(\cos(x-\var{c}))$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\cos(x)$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $\cos(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the left by $\var{c}$ units.}
\choice*{Shifting the graph of $\cos(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\var{c}\cos(x)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\cos(x)$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $\cos(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice*{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-\cos(x)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\cos(x)$?
}
\choice{Shifting the graph of $\cos(x)$ upwards.}
\choice{Shifting the graph of $\cos(x)$ downwards.}
\choice{Shifting the graph of $\cos(x)$ to the left.}
\choice{Shifting the graph of $\cos(x)$ to the right.}
\choice*{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically.}
\choice{Stretching the graph of $\cos(x)$ vertically
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-\var{c}\cos(x)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\cos(x)$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $\cos(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\cos(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\cos(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\cos(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$.}
\choice*{Stretching the graph of $\cos(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}
\end{topic}









\begin{topic}{Transformations of trigonometric functions}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)+c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)$?
}
\choice*{Shifting the graph of $\sin(x)$ upwards by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ downwards by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ to the left by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $c$.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)-c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)$?
}
\choice{Shifting the graph of $\sin(x)$ upwards by $c$ units.}
\choice*{Shifting the graph of $\sin(x)$ downwards by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ to the left by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $c$.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x+c)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)$?
}
\choice{Shifting the graph of $\sin(x)$ upwards by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ downwards by $c$ units.}
\choice*{Shifting the graph of $\sin(x)$ to the left by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $c$.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x-c)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)$?
}
\choice{Shifting the graph of $\sin(x)$ upwards by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ downwards by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ to the left by $c$ units.}
\choice*{Shifting the graph of $\sin(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $c$.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)+c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)$?
}
\choice{Shifting the graph of $\sin(x)$ upwards.}
\choice{Shifting the graph of $\sin(x)$ downwards.}
\choice{Shifting the graph of $\sin(x)$ to the left.}
\choice{Shifting the graph of $\sin(x)$ to the right.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice*{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically.}
\choice{Stretching the graph of $\sin(x)$ vertically
and reflecting the result about the $\sin(x)$-axis.}
\end{question}

\begin{question}{Multiple Choice}
\qutext{
Let $c$ be a positive real number.
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)+c$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $g(x)=-c\sin(x)$?
}
\choice{Shifting the graph of $\sin(x)$ upwards by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ downwards by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ to the left by $c$ units.}
\choice{Shifting the graph of $\sin(x)$ to the right by $c$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $c$.}
\choice*{Stretching the graph of $\sin(x)$ vertically by the factor $c$
and reflecting the result about the $x$-axis.}
\end{question}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)+\var{c}$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\sin(x)$?
}
\code{
$c=range(1,20,1);
}
\choice*{Shifting the graph of $\sin(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x)-\var{c}$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\sin(x)$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $\sin(x)$ upwards by $\var{c}$ units.}
\choice*{Shifting the graph of $\sin(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(x+\var{c})$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\sin(x)$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $\sin(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ downwards by $\var{c}$ units.}
\choice*{Shifting the graph of $\sin(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=(\sin(x-\var{c}))$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\sin(x)$?
}
\code{
$c=range(1,20,1);
}
\choice{Shifting the graph of $\sin(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the left by $\var{c}$ units.}
\choice*{Shifting the graph of $\sin(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\var{c}\sin(x)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\sin(x)$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $\sin(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice*{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=\sin(-x)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\sin(x)$?
}
\choice{Shifting the graph of $\sin(x)$ upwards.}
\choice{Shifting the graph of $\sin(x)$ downwards.}
\choice{Shifting the graph of $\sin(x)$ to the left.}
\choice{Shifting the graph of $\sin(x)$ to the right.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice*{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically.}
\choice{Stretching the graph of $\sin(x)$ vertically
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-\sin(x)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\sin(x)$?
}
\choice{Shifting the graph of $\sin(x)$ upwards.}
\choice{Shifting the graph of $\sin(x)$ downwards.}
\choice{Shifting the graph of $\sin(x)$ to the left.}
\choice{Shifting the graph of $\sin(x)$ to the right.}
\choice*{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically.}
\choice{Stretching the graph of $\sin(x)$ vertically
and reflecting the result about the $x$-axis.}
\end{question}


\begin{question}{Multiple Choice}
\qutext{
How can we obtain the graph of the function
$g:\mathbb{R}\to\mathbb{R}$, $g(x)=-\var{c}\sin(x)$ from the graph of
$f:\mathbb{R}\to\mathbb{R}$, $f(x)=\sin(x)$?
}
\code{
$c=range(2,20,1);
}
\choice{Shifting the graph of $\sin(x)$ upwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ downwards by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the left by $\var{c}$ units.}
\choice{Shifting the graph of $\sin(x)$ to the right by $\var{c}$ units.}
\choice{Reflecting the graph of $\sin(x)$ about the $x$-axis.}
\choice{Reflecting the graph of $\sin(x)$ about the $y$-axis.}
\choice{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$.}
\choice*{Stretching the graph of $\sin(x)$ vertically by the factor $\var{c}$
and reflecting the result about the $x$-axis.}
\end{question}
\end{topic}

\end{document}
