%% Math 131 Midterm 1, Fall 2004
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,epic,eepic,pstcol,graphicx}

%\usepackage{my_teach}

%\pagestyle{myheadings}
\markright{MATH 133, section 1, Midterm 1}

\setlength{\textwidth}{6.5in}
\setlength{\oddsidemargin}{0in}
\setlength{\textheight}{8.5in}

\newcommand{\Blank}{$\underline{\phantom{Please write your name in this
        space}}$} 
\newcommand{\Strut}{$\vphantom{\Big|}$}

\begin{document}

\begin{center}

\textbf{College of the Holy Cross, Fall Semester, 2017} \\
\textbf{MATH 133 Midterm 1} \\
\textbf{Friday, September 22}
\end{center}

\vfil

\noindent\textbf{Your Name}: \Blank
\vskip 0pt plus .3fil

\paragraph{Instructions} Please write your answers in the spaces
provided, and show work on the test itself. Use the back of the
preceding page if you need more space for scratch work.  There are
100 possible points distributed as below.

\vfil

\noindent\textbf{Please do not write in the space below}

\begin{center}
\begin{tabular}{|l||r|}
\hline
Problem & Points/Poss    \Strut \\
\hline\hline
1  & \hfil/\  20\hfil \Strut \\
\hline
2  & \hfil/\  20\hfil \Strut \\
\hline
3  & \hfil/\  20\hfil \Strut \\
\hline
4  & \hfil/\  20\hfil \Strut \\
\hline
5  & \hfil/\  20\hfil \Strut \\
\hline\hline
Total   & \hfil/100\hfil \Strut \\
\hline
{\rm Extra Credit}  & \hfil/\  10\hfil \Strut \\
\hline
\end{tabular}
\end{center}

\vfil\eject

\begin{enumerate}

\item{} 
\begin{enumerate}
\item[(a)] (10) Express the set of all $x$ satisfying $|3x - 9| \le 6$ as an interval or union of intervals.

\vskip 3.0truein

\item[(b)] (10) What is the domain of the function $\displaystyle{f(x) = \frac{\sqrt{3-x}}{x}}$?  Any correct form is OK.
\end{enumerate}
\vfil
\eject 
\item{} (20) The graph $y=f(x)$ and four graphs obtained by transforming it
  are shown in Figures 1 and 2. Match the given formulas with the corresponding graph.
  
\begin{figure}
\begin{center}
\includegraphics[width=40mm]{Orig.png}
\end{center}
\caption{The graph $y = f(x)$}
\end{figure}

\begin{figure}
\centering
\begin{tabular}{cc}
(A) \includegraphics[width=39mm]{M1PA.png}&(B) \includegraphics[width=39mm]{M1PD.png}\\
(C) \includegraphics[width=39mm]{M1PC.png}&(D) \includegraphics[width=39mm]{M1PB.png}
\end{tabular}
\caption{The transformed graphs}
\end{figure}
 
  (a) $y=f(\frac{1}{2}x)$:$\underline{\qquad\qquad}$ \hfil 
  (b) $y=\frac{1}{2}f(x)$:$\underline{\qquad\qquad}$ \hfil 
  (c) $y=f(2x)$:$\underline{\qquad\qquad}$ \\
  (d) Note that there is an extra graph that does not match any of the formulas.  {\it Circle it.}


\vfil
\eject

\item{}
\begin{enumerate}
\item[(a)] (15) Complete the square:  $q(x) = 4x^2 - 16x + 24$.
\vskip 3.0truein
\item[(b)] (5) What is the minimum value of $q(x)$?  
\end{enumerate}

\vfil\eject

\item{} The temperature~$f(t)$ at a desert location varies
  sinusoidally from a low of~$40^\circ\textrm{F}$ at $t = 0$ hours (midnight) to a high
  of~$80^\circ\textrm{F}$ at $t = 12$ hours (noon).  (See graph in Figure 3, which shows
the temperature over two complete days.)
  

 \begin{figure}
\begin{center}
\includegraphics[width=3.0in]{Sinus.png}
\end{center}
\caption{Graph of temperature as a function of time.  }
\end{figure}
\vglue 10pt
\begin{enumerate}
\item[(a)] (6)  What is the period of this sinusoidal oscillation?  $\underline{\qquad\qquad}$ \hfil
\item[(b)] (6)  What is the amplitude? $\underline{\qquad\qquad}$ \hfil
\item[(c)] (8) Give a possible formula for $f$ as a function of $t$.
\end{enumerate}
\vfil\eject
\item{}  You are traveling on a horse along a straight line road starting from $x = 0$ (miles) 
at time $t = 0$ (hours).  For the first two hours, you move in the positive $x$-direction at 5 miles per hour.  At $t = 2$, you realize you have dropped an important item from your saddle bag.  So you turn around and retrace your steps at 5 miles per hour.  You find the item at $t = 3$.  
Then you turn back around and continue at 5 miles per hour for an additional 2 hours.  
\vskip 10pt
\begin{enumerate}
\item[(a)] (10) Sketch the graph of your position $x$ as a function of time $t$ for $0 \le t \le 5$.  
\vglue 3.0truein
\item[(b)]  (10) Give your position $x$ as a piecewise-defined function of $t$.
\end{enumerate}
\vfil\eject
\item{} (Extra Credit) (10) A sample of a radioactive element is decaying over time.  The mass present
at time $t$ is given by 
according to $M(t) = 139 e^{-0.003 t}\ {\rm grams}$, where $t$ is in months.  
Solve the equation $50 = 139 e^{-0.003t}$ for $t$ to find the time when the mass reaches 50 grams.  
\vfil\eject
\end{enumerate}


\end{document}


