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{\LARGE{
\hfil Math 120 A, B Winter 2013 \hfil \pp
\hfil Mid-Term Exam Number Two\hfil  \pp
\hfil February 28, 2013 \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
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{\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}
}
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\vfil
\begin{itemize}
\item Complete all four questions. 
\item Show all work for full credit. 
\item You may use a scientific calculator during this
examination.  Graphing calculators are not allowed.
Also, 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 Robert starts walking due south from a point in the desert at 7 AM.
He walks at a constant speed of 3 km/hr.

Starting at the same time, Frida starts walking from a point 5 km south and 6 km west of 
Robert's starting point.  Frida walks along a straight line which passes through Robert's starting point.
Frida walks at a constant speed to 4 km/hr.

When will Frida and Robert be closest together?  Give your answer in hours after 7 AM.

\newp

\item The population of the city of Rud doubles every 35 years.
The population of the city of Yum increases by 2.3\% every year.

In the year 2000, Yum had a population of 12,000. 

Rud had a population of 19,000 in the year 1995.
 
When will the population of Yum be double that of the population of Rud?
Give your answer in years after 2000.

\newp

\item Let $f(x)$ be a linear-to-linear rational function. Suppose $f(1)=2$, $f(2)=3$ and $f(11)=5$.

\begin{enumerate}
\item  Find $f(10)$.

\vfil
\vfil

\item Find the fixed points of $f$.

\end{enumerate}

\newp

\item Let $g(x)=\sqrt{x}+\sqrt{x-1}.$

\begin{enumerate}

\item Suppose $f(x)$ is a function whose graph is the graph of $g(x)$ shifted 3 units to the right and 4 units down.
Write the rule for $f(x)$.

\vfil

\item Find the inverse function of the function you found in part (a).  
You do not have to specify the domain.

\vfil

\end{enumerate}



\end{enumerate}

\end{document}


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