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\begin{document}
\noindent
\vfil \noindent

{\LARGE{
\hfil Math 120 - Autumn 2016 \hfil \pp
\hfil Final Exam\hfil  \pp
\hfil December 10, 2016 \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 & 15 &\hspace{10mm} \hfil\\ \hline  %multipart
 2 & 16 &       \\ \hline %parametric
 3 & 14 &      \\ \hline %exponential
4 & 14 &    \\ \hline %angelica
5 & 15 &    \\ \hline %linear-to-linear
6 & 14 &    \\ \hline %mereen
7 & 12 &    \\ \hline %essun
Total & 100 & \\ \hline 
\end{tabular}
}
\end{center}
\vfil
\begin{itemize}
\item This exam consists of SEVEN problems on EIGHT pages, including this cover sheet.
\item Show all work for full credit. 
\item You may use a TI-30X IIS calculator during this
exam.  Other calculators and electronic device are not permitted.
\item You do not need to simplify your answers.
\item If you use a trial-and-error or guess-and-check method
when a more rigorous method is available, you will not receive full credit.
\item If you write on the back of the page, please indicate that you have done so!
\item \textbox{Draw a box} around your final answer to each problem.
\item You may use one hand-written double-sided 8.5" by 11" page of notes.
\item You have 170 minutes to complete the exam.
\end{itemize}

\vfil

\newpage

\begin{enumerate}

\item {\bf[5 points per part]} For parts (a) through (c), consider the following multipart function:
$$f(x) = \begin{cases}
1+\sqrt{9-x^2} & \mbox{if } -3 \leq x < 0\\
2x & \mbox{if } 0 \leq x \leq 2\\
1 & \mbox{if } 2 < x \leq 4\\
\end{cases}$$
\begin{enumerate}

\item Sketch a graph of $f(x)$.
\vspace{-.3 in}
\begin{center}
\begin{tikzpicture}
\graphgrid{-4}{5}{-1}{5}{$x$}{$f(x)$}
\end{tikzpicture}
\end{center}

\item Find all values of $x$ such that $f(x) = -2x + 2.2$.

\vskip 2.5 in

\item Let $g(x)$ be the function found by taking the graph of $f(x)$ and shifting it 1 unit left.\\[.1 in]
Write the multipart rule for $g(x)$.

\end{enumerate}

\newpage

\item \begin{enumerate}
\item {\bf [4 points]} A mysterious red dot is moving through the $xy$-plane at a constant speed.\\[.1 in]
At time $t=0$, it starts at $(-1,-1)$. It moves in a straight line towards the point $(31,13)$, reaching it in 10 seconds.\\[.1 in]
Write parametric equations for the red dot's coordinates after $t$ seconds.
\vskip 1.5 in
\item {\bf [5 points]} Fungo is also moving in the $xy$-plane. At time $t=0$, he starts at $(2,6)$.\\[.1 in]
Fungo runs in a straight line towards $(8,-2)$ at a speed of 2 units per second.\\[.1 in]
Write parametric equations for Fungo's coordinates after $t$ seconds.
\vskip 2.5 in
\item {\bf [7 points]} When is Fungo closest to the red dot?

\end{enumerate}

\newpage

\item The population of Threeattle triples every ten years.\\[.1 in]
Four years from now, there will be 10,000 more people in Threeattle than there are today.

\begin{enumerate}
\item {\bf [6 points]} Write a function $f(x)$ for the population of Threeattle $x$ years from today.
\vskip 4 in
\item {\bf [6 points]} Compute the inverse of the function you found in part (a).
\vfill
\item {\bf [2 points]} In one sentence, explain the meaning of the inverse function you found.

\end{enumerate}

\newpage

\item {\bf [14 points]} Angelica and Eliza are standing 100 meters apart, and Peggy is standing exactly halfway between them. Somewhere else in between them is a tree.\\[.1 in]
From where they stand, Angelica, Eliza, and Peggy all measure the angle of elevation of the top of the tree above the ground.\\[.1 in]
Angelica measures it to be $32^\circ$. Eliza measures it to be $27^\circ$.\\[.1 in]
What measurement does Peggy get?

\newpage

\item $f(x)$ is a linear-to-linear rational function whose graph has a horizontal asymptote of $y=5$ and passes through the points $(1,-10)$ and $(2,-35)$.
\begin{enumerate}
\item {\bf [7 points]} Write a formula for $f(x)$.
\vskip 4.5 in
\item {\bf [2 points]} What is the domain of $f(x)$?
\vskip 1 in
\item {\bf [6 points]} Let $g(x) = f(f(x))$. Find the asymptotes of $g(x)$.
\end{enumerate}

\newpage

\item {\bf [14 points]} The temperature in Meereen is a sinusoidal function of time.\\[.1 in]
The temperature will decrease for the next 5 years until it reaches a minimum of $20^\circ$. Then the temperature will climb until 21 years from now, when it reaches a maximum of $80^\circ$.\\[.1 in]
Dany is unhappy when the temperature in Meereen is below $70^\circ$. Over the next 100 years, for how long will she be unhappy?

\newpage

\item \begin{enumerate}
\item {\bf [12 points]} Essun is running 3 meters per second clockwise around a circular track.\\[.1 in]
From her starting point, it takes her 9 seconds to reach the northernmost point of the track, and then an additional 13 seconds to reach the easternmost point of the track.\\[.1 in]
After 2 minutes, how far east is Essun from the westernmost point of the track?

\vfill

\item {\bf [0 points]} You're done! Please check your work, then enjoy this celebratory maze.

Help Essun get to the exit. Unfortunately, after spending so much time running clockwise, she has forgotten how to turn left.

\begin{center}
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(2,0) -- (2,11) -- (7,11) -- (7,6) -- (4,6) -- (4,8) -- (6,8) -- (6,6)
(3,7) -- (5,7) -- (5,5) -- (3,5) -- (3,9) -- (11,9) -- (11,7) -- (9,7) -- (9,10) -- (12,10) -- (12,6) -- (7,6)
(2,10) -- (5,10) -- (5,8)
(2,8) -- (3,8)
(2,4) -- (6,4)
(4,5) -- (4,3) -- (10,3) -- (10,5) -- (9,5) -- (9,4)
(8,6) -- (8,11) -- (14,11) -- (14,8)
(14,6) -- (17,6) -- (17,9) -- (15,9) -- (15,11) -- (20,11) -- (20,2) -- (16,2) -- (16,4) -- (20,4)
(9,3) -- (9,2) -- (15,2) -- (15,3)
(13,2) -- (13,3)
(10,9) -- (10,8) -- (15,8) -- (15,9)
(14,6) -- (14,7) -- (15,7) -- (15,3) -- (20,3)
(8,4) -- (13,4) -- (13,6) -- (12,6)
(13,6) -- (14,6) -- (14,5) -- (11,5) -- (11,3) -- (13,3) -- (13,4)
(11,5) -- (11,6)
(13,8) -- (13,10) -- (16,10) -- (16,7) -- (19,7) -- (19,9) -- (18,9) -- (18,6) -- (20,6)
(18,3) -- (18,5) -- (16,5) -- (16,4)
(16,10) -- (17,10) -- (17,11)
(18,11) -- (18,10) -- (20,10)
(14,2) -- (14,5)
(6,9) -- (6,11)
(19,4) -- (19,6)
(4,3) -- (3,3) -- (3,4)
(6,4) -- (7,4) -- (7,5)
(12,7) -- (13,7) -- (13,8);

\node [anchor=west] at (2.5,1) {START};
\node [anchor=west,rotate=90] at (1,2.5) {FINISH};
\draw [thick,->] (2.5,1) arc (270:180:.5);
\draw [thick,->] (1.5,2) arc (270:180:.5);

\end{tikzpicture}
\end{center}

\end{enumerate}

\end{enumerate}

\end{document}