%% This document created by Scientific Notebook (R) Version 3.0


\documentclass[12pt,thmsa]{article}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{sw20jart}

%TCIDATA{TCIstyle=article/art4.lat,jart,sw20jart}

%TCIDATA{<META NAME="ViewSettings" CONTENT="17">}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 11:09:17 1997}
%TCIDATA{CSTFile=Exam.cst}
%TCIDATA{PageSetup=72,72,36,36,0}
%TCIDATA{AllPages=
%F=36,\PARA{038<p type="texpara" tag="Body Text" >\hfill \thepage}
%}


\input{tcilatex}
\begin{document}


\section{Exam}

\subsection{Text}

\section{Functions and Symmetries}

Your Name: 
%TCIMACRO{\HTML{<Input TYPE="Text" NAME="STUDENTNAME" VALUE=" " SIZE=0>}}
%BeginExpansion
%%
%EndExpansion

\vspace{1pt}

\subsection{Setup}

$\limfunc{num}=\limfunc{rand}(1,10)$ [$\limfunc{num}$ will generate
numerators for the fraction problems]

$\limfunc{den}=\limfunc{rand}(2,10)$ \ [$\limfunc{den}$ will generate
denominators]

Choice Space: 2

Choices:\ No Break, Radio Buttons, Permute

Title:Functions and Symmetry

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-10,10)$

$b:=\limfunc{rand}(-5,5)$

$f_{1}:=a\sin bx$

$f_{2}:=a\cos bx$

Conditions: $\left( ab\neq 0\right) $

\subsection{Statement}

Which function is even?

\subsection{Choices}

\begin{itemize}
\item  \FRAME{itbpF}{3in}{2in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2in;depth 0in;display
"USEDEF";function \TEXUX{$f_{1}$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";xviewmin
"-5";xviewmax "5";yviewmin "-5.2";yviewmax "5.204";phi 45;theta 45;plottype
4;numpoints 49;axesstyle "normal";xis \TEXUX{fQSUB1ESUB};var1name
\TEXUX{$x$};}}

\item  \FRAME{itbpF}{3in}{2in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2in;depth 0in;display
"USEDEF";function
\TEXUX{$f_{2}\QTO{correctchoice}{\correctchoice{}}$};linecolor
"black";linestyle 1;linethickness 1;pointstyle "point";xmin "-5";xmax
"5";xviewmin "-5";xviewmax "5";yviewmin "-5.2";yviewmax "5.204";phi 45;theta
45;plottype 4;numpoints 49;axesstyle "normal";xis
\TEXUX{fQSUB2ESUB};var1name \TEXUX{$x$};}}$\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\subsection{Answer}

$%
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$

\subsection{Solution}

$%
%TCIMACRO{\FORMULA{f_{2}}{f_{2}}{evaluate}}
%BeginExpansion
f_{2}%
%EndExpansion
$ is even and $%
%TCIMACRO{\FORMULA{f_{1}}{f_{1}}{evaluate}}
%BeginExpansion
f_{1}%
%EndExpansion
$ is odd.

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-5,5)$

$b:=\limfunc{rand}(-5,5)$

$O:=1+\frac{\limfunc{num}}{\limfunc{den}}$

Conditions: $\left( ab\neq 0\right) \wedge \left( \left| ab\right| \neq
1\right) $

\subsection{Statement}

The following plot is

\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"USEDEF";function \TEXUX{$\left( a\sin \left( Ot+1\right) ,b\cos \left(
Ot\right) \right) $};linecolor "black";linestyle 1;linethickness
1;pointstyle "point";xmin "-5";xmax "5";xviewmin "-2.08";xviewmax
"2.082";yviewmin "-3.119";yviewmax "3.122";rangeset"X";phi 45;theta
45;plottype 19;labeloverrides 3;x-label "x";y-label "y";numpoints
49;axesstyle "normal";xis \TEXUX{t};var1name \TEXUX{$x$};}}

\subsection{Choices}

\begin{itemize}
\item  symmetric with respect to the $y$-axis

\item  symmetric with respect to the origin$\correctchoice{}$

\item  symmetric with respect to the $x$-axis
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\subsection{Answer}

symmetric with respect to the origin

\subsection{Solution}

By reflecting points through the axes and origin, you can determine the
symmetry.

\section{Question}

\subsection{Setup}

$a:=\limfunc{rand}(-2,2)$

$b:=\limfunc{rand}(-5,5)$

Conditions: $\left( ab\neq 0\right) $

\subsection{Statement}

Which of the following is the graph of $%
%TCIMACRO{
%\FORMULA{y=\left( x-a\right) ^{2}+b}{y=\left( x-a\right) ^{2}+b}{evaluate}}
%BeginExpansion
y=\left( x-a\right) ^{2}+b%
%EndExpansion
$?

\subsection{Choices}

\begin{itemize}
\item  \FRAME{itbpF}{3in}{2.0003in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0in;display
"USEDEF";function \TEXUX{$\left( x+a\right) ^{2}+b$};linecolor
"black";linestyle 1;linethickness 1;pointstyle "point";xmin "-5";xmax
"5";xviewmin "-5";xviewmax "5";rangeset"X";phi 45;theta 45;plottype
4;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}

\item  \FRAME{itbpF}{3in}{2.0003in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0in;display
"USEDEF";function \TEXUX{$\left( x-a\right)
^{2}+b\QTO{correctchoice}{\correctchoice{}}$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";xviewmin
"-5";xviewmax "5";rangeset"X";phi 45;theta 45;plottype 4;numpoints
49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}$\correctchoice{}$

\item  \FRAME{itbpF}{3in}{2.0003in}{0in}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0in;display
"USEDEF";function \TEXUX{$\left( x-a\right) ^{2}-b$};linecolor
"black";linestyle 1;linethickness 1;pointstyle "point";xmin "-5";xmax
"5";xviewmin "-5";xviewmax "5";rangeset"X";phi 45;theta 45;plottype
4;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name \TEXUX{$x$};}}
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\subsection{Answer}

\FRAME{itbpF}{3in}{2in}{0in}{}{}{}{\special{language "Scientific Word";type
"MAPLEPLOT";width 3in;height 2in;depth 0in;display "USEDEF";function
\TEXUX{$\left( x-a\right) ^{2}+b$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";phi 45;theta
45;plottype 4;numpoints 49;axesstyle "normal";xis \TEXUX{x};var1name
\TEXUX{$x$};}} is the plot of $%
%TCIMACRO{
%\FORMULA{y=\left( x-a\right) ^{2}+b}{y=\left( x-a\right) ^{2}+b}{evaluate}}
%BeginExpansion
y=\left( x-a\right) ^{2}+b%
%EndExpansion
$

\subsection{Solution}

The graph is symmetric with respect to the line $%
%TCIMACRO{\FORMULA{x=a}{x=a}{evaluate}}
%BeginExpansion
x=a%
%EndExpansion
$ and has a minimum at the point $\left( 
%TCIMACRO{\FORMULA{a}{a}{evaluate}}
%BeginExpansion
a%
%EndExpansion
,%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
\right) $.

\end{document}
