\documentclass[12pt]{exam}
\newcommand{\answer}
{\noindent \hspace{1in}\hbox to 4.5in{Answer:\enspace\hrulefill} 
\vspace{0.2in}}
\usepackage{amsmath}
\addtolength{\topmargin}{0.5in}
\addtolength{\textheight}{-0.5in}
\begin{document}

% \pointsinmargin 
\pointname{ pts}
\marginpointname{ pts}
\addpoints 

\noindent
\textbf{Math 105 Exam I.}
\hspace{1.6in}
\hbox to 3.3in{Name:\enspace\hrulefill}

\vspace{0.2in}

\noindent
February 2, 1999
\hspace{1.9in}
\hbox to 3.3in{Instructor's name:\enspace\hrulefill}

\vspace{0.2in}

\noindent
\hspace{3.15in}
\hbox to 3.3in{Time of MWF class:\enspace\hrulefill}

\vspace{0.2in}

Show all work and put your answers in the spaces provided.  You will
receive no credit if the answer is not in the space provided and no
partial credit for a wrong answer if you do not show your work.
Answers may be approximated by decimals if desired, but full points
will be also be awarded for correct answers left in exact form as
fractions.

\vspace{0.2in}

\noindent 
Sections of the course: 
\begin{tabbing}
Section 01 \hspace{0.2in}  \= Brown  \hspace{0.2in} \= MWF
10:40-11:30 am \\
Section 02                 \> Palmieri \> MWF 1:55-2:45 pm
\end{tabbing}

\newpage

\begin{questions}

%%%%%%%%%%%%%%%%

\question[6] Suppose that a baker can sell a cake for \$7, so the
revenue function is $R(q) = 7q$.  The baker estimates the cost of
making $q$ cakes to be $C(q) = 2q+600$.  What is the baker's profit
function?

\vspace{1.5in}

\answer

%%%%%%%%%%%%%%%%

\question[4] What is the $y$-intercept of the line $-3x + 4y = 2$?

\vspace{1in}

\answer 

%%%%%%%%%%%%%%%%

\question[4] What is the slope of the line through the points $(1,1)$ and
$(3,-5)$?

\vspace{1in}

\answer 

%%%%%%%%%%%%%%%%

\question[6] What is the equation of the line which goes through the
point $(0,3)$ and which is parallel to the line $y=-4x+5$?

\vspace{1.3in}

\answer 

%%%%%%%%%%%%%%%%

\question[5] Let $\displaystyle f(x) = \frac{x-7}{x+1}$.  Find $f(a+2)$.

\vspace{1.5in}

\answer 

%%%%%%%%%%%%%%%%

\question[8] Let $f(x)=2x^{2} - 8x - 5$.  Complete the square in this
quadratic function.  (We are looking for an answer of the form ``$f(x)
= A (x+B)^{2} + C$''.)

\vspace{3in}

\answer 

%%%%%%%%%%%%%%%%

\question[5] Find the domain of the function $f(x) = \sqrt{x+3}$.

\vspace{1.5in}

\answer 

%%%%%%%%%%%%%%%%

\newpage

\question[5] Compute $\displaystyle (1/8)^{2/3}$.
Express your answer as a fraction.

\vspace{1.5in}

\answer 

%%%%%%%%%%%%%%%%

\question A local theater owner realizes that when she charges \$18
per ticket, she averages 200 people per night.  When she raises prices
to \$21, the attendance drops to 170.  Let $p$ denote the ticket
price, and let $q$ denote the demand (the attendance).  

\begin{parts}

\part[6] Assuming that the demand is a linear function of the price,
write demand in terms of price.

\vspace{2in}

\answer 

\part[2] If the theater holds 260 people, how much should the owner
charge in order to fill the theater to capacity?

\vspace{1.5in}

\answer 

\end{parts}

%%%%%%%%%%%%%%%%

\question[6] A businessman selling widgets determines that the price $p$
of widgets and the demand $q$ for widgets are related by the function
$p=-6q+1300$.  Determine the revenue function $R(q)$ in terms of the
demand $q$.

\vspace{1.5in}

\answer 

%%%%%%%%%%%%%%%%

\question[8] A baseball cap company has a profit function of
\[
-100p^{2} + 1800p - 7200,
\]
where $p$ is the price charged per cap.  How much should they charge
to maximize profit?

\vspace{2.5in}

\answer 

%%%%%%%%%%%%%%%%

\newpage

\question[7] Use the quadratic formula to solve the equation
\[
2x^{2} +x - 6 = 0.
\]

\vspace{1.5in}

\answer 

%%%%%%%%%%%%%%%%

\question Consider the function
\[
f(x) = \frac{2(x+2)}{x^{2}-4x+3} = \frac{2(x+2)}{(x-3)(x-1)}.
\]

\begin{parts}

\part[4] Find the vertical asymptotes of $f(x)$, or write ``none'' if
there aren't any.

\vspace{1.5in}

\answer 

\part[4] Find the horizontal asymptotes of $f(x)$, or write ``none'' if
there aren't any.

\vspace{1.5in}

\answer 

\end{parts}

%%%%%%%%%%%%%%%%

\question The line $x=2$ is a vertical asymptote of the function 
\[
f(x) = \frac{x+1}{x-2}.
\]

\begin{parts}

\part[2] Does this curve climb or fall as it approaches the asymptote
from the left? 

\vspace{2in}

\answer 

\part[2] Does this curve climb or fall as it approaches the asymptote
from the right? 

\vspace{1.5in}

\answer 

\end{parts}

%%%%%%%%%%%%%%%%

\question[4] Let 
\[
f(x) = \frac{3x-4}{2x-1}.
\]
Find the horizontal asymptotes of $f(x)$.

\vspace{1.5in}

\answer 

%%%%%%%%%%%%%%%%

\question[6] A certain sling-shot will fire a ball straight up in the air
at a speed of 160 feet/second.  The height of the ball after $t$
seconds is given by the formula
\[
h(t) = -16 t^{2} + 160 t.
\] 
What is the maximum height that the ball reaches?

\vspace{2in}

\answer 

%%%%%%%%%%%%%%%%

\question[6] Consider the function 
\[
f(x) = \begin{cases}
3x+1      & \text{if $x \leq 0$} \\
x^{2} + 1 & \text{if $0 < x \leq 1$} \\
2-x^{2}   & \text{if $x>1$}.
\end{cases}
\] 
Is the function continuous?  If not, give the $x$-values for its
discontinuities.

\vspace{2.5in}

\answer 

%%%%%%%%%%%%%%%%

\end{questions}

\end{document}

