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{\Large TEST 1

Math 128 - R5}
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You have 50 minutes to complete the test.
Show all relevant work (or else no credit).  
Make your work legible, if I can't read it, I can't grade it.  
Each problem is worth 10 points.
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Name \rule{5in}{.2pt}

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\begin{enumerate}

\item  The following function is used to determine a persons water bill:
\[
C(x) = \left\{
\begin{array}{ll}
1.5x & 0 \leq x \leq 100 \\
1.5x +1.2(x-100) & 100 < x \leq 1000 \\
1000 + .7(x-1000) & x > 1000 \\
\end{array}
\right.
\]
Where $C(x)$ is the cost in dollars for $x$ thousand gallons of water.
\begin{enumerate}
\item  What is $C(200)$?
\item  Write a sentence explaining what $C(200)$ means.
\end{enumerate}

\item  Find the equation of the line through the points: $(2,5), (5,-3)$.

\item  \label{t-shirt}  
You decide to start a T-shirt business.
Just starting out, you only offer one type of T-shirt and that will 
sell for \$15 each.
You make the T-shirts at your home so there is no building to rent,
but you do set up a new phone line, a 1-800 number and a 1-900 number.
This phone line costs \$115 per month.
You are able to produce each shirt for \$7 each.
\begin{enumerate}
\item  What is the cost function $C(x)$ for this business?
\item  What is the revenue function $R(x)$ for this business?
\item  What is the Profit function $P(x)$?
\item  If you sell 10 shirts, do you make or lose money, and how much?
\end{enumerate}

\item  In your T-shirt business of problem~\ref{t-shirt},
you figure that your business worth can be modeled by the equation:
\[
W=2500+1200t
\]
where $W$ is the worth of the business in dollars,
and $t$ is the number of years past 1998 
(you start the business in January 1998).
In what year do you project your business to be worth \$9100?

\item If $f(x)=x^2-x$, find, and simplify, $\frac{f(x+h)-f(x)}{h}$.

\item  If $f(x)=\frac{1}{x-1}$ and $g(x)=x^3-x^2$, 
find, $f\circ g(x)$. (You don't need to simplify it).

\item  Graph the line $3x-2y=6$



\end{enumerate}


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