% Note:  Taken from the ASU math department web site.

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\begin{document}

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\centerline{\textbf{\large Exam \#1 $\cdot$ Tuesday Sep. 13, 2005}}
\vspace*{.2in}
MATH 110 $\cdot$ Section 10 $\cdot$ Fall 2005  \hspace*{0.5in} Name \hrulefill
\vspace*{0.2in}
\begin{enumerate}

%% ----------------------------------------------------------------
\item[1.] Which of the following tables determine $y$ as a function of $x$?

\begin{tabular}{lll}
	(1)
	\begin{tabular}{|r||r|r|r|r|}
	\hline $x$ &  1 &  2 &  3 & 4 \\
	\hline $y$ & -1 &  0 & -1 & 1 \\
	\hline
	\end{tabular}
\qquad \qquad
	(2)
	\begin{tabular}{|r||r|r|r|r|}
	\hline $x$ &  0 &  2 &  4 & 2 \\
	\hline $y$ &  2 &  7 & -6 & 4 \\
	\hline
	\end{tabular}
\qquad \qquad
	(3)
	\begin{tabular}{|r||r|r|r|r|}
	\hline $x$ &  5 &  4 &  2 & 1 \\
	\hline $y$ &  4 &  4 &  4 & 4 \\
	\hline
	\end{tabular}
\end{tabular}

\vspace*{0.125in}

\begin{tabular}{lll}
(A) 3 only \qquad\qquad &
(B) 1 and 2 only \qquad\qquad &
(C) 2 and 3 only \\
(D) 1 and 3 only \qquad\qquad&
(E) All of them \\
\end{tabular}

\vspace*{1.5in}

%% ----------------------------------------------------------------
\item[2.] Which of the following tables determine $x$ as a function of $y$?

\begin{tabular}{lll}
	(1)
	\begin{tabular}{|r||r|r|r|r|}
	\hline $y$ & -1 &  0 & -1 & 1 \\
	\hline $x$ &  1 &  2 &  3 & 4 \\
	\hline
	\end{tabular}
\qquad \qquad
	(2)
	\begin{tabular}{|r||r|r|r|r|}
	\hline $y$ &  2 &  7 & -6 & 4 \\
	\hline $x$ &  0 &  2 &  4 & 2 \\
	\hline
	\end{tabular}
\qquad \qquad
	(3)
	\begin{tabular}{|r||r|r|r|r|}
	\hline $y$ &  4 &  4 &  4 & 4 \\
	\hline $x$ &  5 &  4 &  2 & 1 \\
	\hline
	\end{tabular}
\end{tabular}

\vspace*{0.125in}

\begin{tabular}{lll}
(A) 1 and 2 only \qquad\qquad &
(B) 1 only \qquad\qquad&
(C) 2 only \\
(D) All of them  \qquad\qquad &
(E) None of them \\
\end{tabular}

\vspace*{1.5in}

%% ----------------------------------------------------------------
\item[3.] Which of the following equations determine $y$ as a function of $x$?

\begin{tabular}{lll}
	(1) $y   = x + 1$
\qquad \qquad
	(2) $y^2 = x + 1$
\qquad \qquad
	(3) $y^3 = x + 1$
\end{tabular}

(Hint:  For each of these curves, how many $y$'s lie on the curve at $x=0$?
What about at other values of $x$?)

\vspace*{0.125in}

\begin{tabular}{lll}
(A) All of them \qquad\qquad&
(B) 1 and 2 only \qquad\qquad &
(C) 3 only \\
(D) 1 and 3 only &
(E) 2 and 3 only \\
\end{tabular}

\vspace*{2.0in}

%% ================================================================
\newpage
%% ----------------------------------------------------------------
\item[4.] Which of the following graphs represent $y$ as a function of $x$?

\begin{tabular}{ccccc}
(Graph 1) & \qquad \qquad \qquad \qquad & (Graph 2) & \qquad \qquad \qquad \qquad & (Graph 3) \\
%\includegraphics{exam_01_fig_03.eps} & &
%\includegraphics{exam_01_fig_04.eps} & &
%\includegraphics{exam_01_fig_05.eps} \\
\end{tabular}
\vspace*{2.0in}

\begin{tabular}{lll}
(A) All of them \qquad\qquad&
(B) 1 and 3 only \qquad\qquad &
(C) 3 only \\
(D) 1 and 2 only &
(E) 2 and 3 only \\
\end{tabular}

\vspace*{2.0in}

%% ----------------------------------------------------------------
\item[5.] Find the domain and zero(s) of the function $f(x) = \sqrt{x-5}$.

\vspace*{2.0in}

%% ----------------------------------------------------------------
\item[6.] Find the domain and zero(s) of the function $f(x) = x^2 + 3x + 2$.

\vspace*{2.0in}

%% ================================================================
\newpage
%% ----------------------------------------------------------------
\item[7.] Find the domain and zero(s) of the function
$f(x) = \frac{x+5}{x^2+4x+4}$.

\vspace*{2.0in}

%% ----------------------------------------------------------------
\item[8.] Find the domain and range of the following function:

%\begin{center}
%\includegraphics{exam_01_fig_01.eps}
%\end{center}
\vspace*{1.0in}

\vspace*{1.5in}

%% ----------------------------------------------------------------
\item[9.] Determine the $x$-intercept(s) and $y$-intercept(s) of the following
function:

%\begin{center}
%\includegraphics{exam_01_fig_02.eps}
%\end{center}
\vspace*{1.0in}

\vspace*{2.0in}

%% ----------------------------------------------------------------
\newpage
\item[10.] Using the space provided below, graph the function
$$f(x) = \left\{\begin{matrix}
	2   & & x < -1 \\
	|x| & & -1 \le x < 2 \\
	-x  & & x \ge 2 \\
\end{matrix}\right.$$

%\begin{center}
%\includegraphics{exam_01_fig_07.eps}
%\end{center}
\vspace*{1.0in}

\vspace*{1.0in}

%%% ----------------------------------------------------------------
%\item[10.] Which of the following functions represents the graph shown?
%
%\begin{center}
%\includegraphics{exam_01_fig_07.eps}
%\end{center}
%
%\begin{tabular}{lll}
%
%(A) $f(x) = \left\{\begin{matrix}
%	2   & & x < -1 \\
%	|x| & & -1 \le x < 2 \\
%	-x  & & x \ge 2 \\
%\end{matrix}\right.$
%\qquad &
%
%(B) $f(x) = \left\{\begin{matrix}
%	2   & & x < -1 \\
%	|x| & & -1 \le x < 2 \\
%	-x  & & x \ge 2 \\
%\end{matrix}\right.$
%\\
%& \\
%
%(C) $f(x) = \left\{\begin{matrix}
%	2   & & x < -1 \\
%	|x| & & -1 \le x < 2 \\
%	-x  & & x \ge 2 \\
%\end{matrix}\right.$
%\qquad &
%
%(D) $f(x) = \left\{\begin{matrix}
%	2   & & x < -1 \\
%	|x| & & -1 \le x < 2 \\
%	-x  & & x \ge 2 \\
%\end{matrix}\right.$
%\\
%& \\
%
%(E) $f(x) = \left\{\begin{matrix}
%	2   & & x < -1 \\
%	|x| & & -1 \le x < 2 \\
%	-x  & & x \ge 2 \\
%\end{matrix}\right.$
%
%\end{tabular}

%% ----------------------------------------------------------------
\item[11.] Let $f(x)$ be given by the following graph:

%\begin{center}
%\includegraphics{exam_01_fig_06.eps}
%\end{center}
\vspace*{1.5in}

(a) Determine the turning points of the function.

\vspace*{1.0in}

(b) Determine the intervals on which the function is increasing.

\vspace*{1.0in}

(c) Determine the intervals on which the function is decreasing.

\vspace*{1.0in}

%% ================================================================
\newpage
%% ----------------------------------------------------------------
\item[12.] Let
$$
f(x) = \left\{\begin{matrix}
	|x| & & x < -1 \\
	3 & & -1 \le x < 1 \\
	x-2 & & x \ge 1 \\
\end{matrix}
\right.
$$

\vspace*{0.1in}

Part (a). Evaluate $f(-2)$.

\vspace*{1.0in}

Part (b). Evaluate $f(-1)$.

\vspace*{1.0in}

Part (c). Evaluate $f(3)$.

\vspace*{1.0in}

%% ----------------------------------------------------------------
\item[13.] Which of the following formulas extends the function
$$
f(x) = \left\{\begin{matrix}
	x^2 - x - 1 && x > 0 \\
\end{matrix}
\right.
$$
to make it an odd function defined on all real numbers?

\vspace*{0.2in}

\begin{tabular}{lll}
(a)
$
\displaystyle
f(x) = \left\{\begin{matrix}
	x^2-x-1 & \quad & x > 0 \\
	0 & \quad & x = 0 \\
	x^2+x+1 & \quad & x < 0 \\
\end{matrix}\right.
$
&
\qquad
&
(b)
$
\displaystyle
f(x) = \left\{\begin{matrix}
	x^2-x-1 & \quad & x > 0 \\
	0 & \quad & x = 0 \\
	x^2-x-1 & \quad & x < 0 \\
\end{matrix}\right.
$
\\
& &
\\
(c)
$
\displaystyle
f(x) = \left\{\begin{matrix}
	x^2-x-1 & \quad & x > 0 \\
	0 & \quad & x = 0 \\
	-x^2+x+1 & \quad & x < 0 \\
\end{matrix}\right.
$
&
\qquad
&
(d)
$
\displaystyle
f(x) = \left\{\begin{matrix}
	x^2-x-1 & \quad & x > 0 \\
	0 & \quad & x = 0 \\
	-x^2-x-1 & \quad & x < 0 \\
\end{matrix}\right.
$
\\
& &
\\
(e) None of these.
\end{tabular}

%% ================================================================
\newpage
%% ----------------------------------------------------------------
\item[14.] You begin a business with initial funds of \$1,000,000.  Your
business is losing money at the rate of \$40,000 per day.

\vspace*{0.1in}

(a) Sketch a graph of your funds as a function of time.

\vspace*{2.0in}

(b) Describe the significance of the $x$ and $y$ intercepts of this function.

\vspace*{1.0in}

%% ----------------------------------------------------------------
\item[15.] You have chosen a certain make and model of vehicle to rent.  Fuel
costs \$0.12 per mile for this make and model of vehicle.  Company A rents the
vehicle for \$25 per day plus \$0.10 per mile.  Company B rents the vehicle for
\$30 per day plus \$0.08 per mile.  Thus, your total cost renting from company
A is \$25 per day plus \$0.10 per mile plus \$0.12 per mile, while your total
cost renting from company B is \$30 per day plus \$0.08 per mile plus \$0.12
per mile.  (Both companies permit one-way trips at no extra expense.)

\vspace*{0.1in}

(a) Find the cost per mile for a day trip, including fuel, using a vehicle from
company A, as a function of the number of miles driven.

\vspace*{1.0in}

%% ================================================================
\newpage
(b) Find the cost per mile for a day trip, including fuel, using a vehicle from
company B, as a function of the number of miles driven.

\vspace*{3.0in}

(c) Suppose Phoenix is 120 miles away and can be reached in a day.  For which
choice of company will you obtain a lower cost?

\vspace*{3.0in}

(d) Suppose San Diego is 400 miles away and can be reached in a day.  For which
choice of company will you obtain a lower cost?

\end{enumerate}
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\end{document}
