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%\markboth{Dr. Matthew M. Conroy - University of Washington}{Dr. Matthew M. Conroy - University of Washington}


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\vfil \noindent

{\LARGE{
\hfil Math 120 A Winter 2017 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil February 23, 2017 \hfil \pp
}}

\normalsize
\vfil
\medskip
\hfil Name: \hrulefill \hrulefill \hspace{0.5in} Student ID no. : \hrulefill

\vfil

\hfil Signature: \hrulefill \hrulefill \hrulefill \hspace{0.5in} Section: \hrulefill 
 
\vfil
\begin{center}
{\Huge
\begin{tabular}{||c|c|r||} \hline 
 1 & 10 &\hspace{10mm} \hfil\\ \hline 
 2 & 10 &       \\ \hline
 3 & 10 &      \\ \hline
4 &  10 &    \\ \hline
Total & 40 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item Complete all four questions. 
\item Show all work for full credit. 
\item The only calculator you may use during this exam is
a TI-30XIIs.
All other electronic devices are not allowed, and should be
turned off and put away for the duration of the exam.
\item If you use a trial-and-error or guess-and-check method
when an algebraic method is available, you will not receive full credit.
\item You may use one hand-written 8.5 by 11 inch page of notes.  Write
your name on your notesheet and turn it in with your exam.
\item You have 50 minutes to complete the exam. 
\end{itemize}
\vfil
.

\newp

\begin{enumerate}

\item You have $1200$ meters of fencing with which to enclose a rectangular piece
of land.  You will also use some of the fencing to partition the enclosure into six sections as shown.

\begin{tikzpicture}
\draw (0,0) -- (5,0) -- (5,3) -- (0,3) --(0,0);
\draw (2,0) -- (2,3);
\draw (3,0) -- (3,3);
\draw (0,1) -- (5,1);
\end{tikzpicture}

What should the dimensions of the rectangle be to enclose the maximal area?


\newp

\item \begin{enumerate}
\item Let $g(x)=x^2+6x+3$ for $x\le -3$.  Find $g^{-1}(x)$.
\vfil
\item Let $f(x)=3x-1$ and $h(x)=x^2-2$.  Find the fixed points of $f(h(x))$.
\end{enumerate}


\newp

\item City A had a population of 2.1 million in the year 2000.
City A's population doubles every 44 years.

City B's population increases at a rate of $2\%$ per year. 
In the year 1990, the population of City B was half the population of City A.

When will the populations of City A and City B be equal? Give you answer in years after the year 2000.

\newp

\item 
\begin{enumerate}
\item Let $f(x)=|2x+1|$.  Give the multipart rule for the function $g(x)$
whose graph is the graph of $f(x)$ shifted $3$ units to the left and $2$ units down.
\vfil
\item Suppose the maximum value of a function $h(x)$ occurs when $x=4$.
For what $x$ value does the maximum value of $\frac{1}{2}h(4x-1)+8$ occur?
\vfil
\item Suppose the domain of $r(x)$ is $-4 \le x \le 5$ and the range of $r(x)$ is $1 \le y \le 8$.
Give the domain and range of $-5r(2-x)-6$.

\end{enumerate}


\end{enumerate}

\end{document}


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