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{\Large TEST 1

Math 1090 - 4}
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You have 1 hour 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:
\[
C(x) = \left\{
\begin{array}{ll}
1.5x & \mbox{ if } 0 \leq x \leq 100 \\
1.5x +1.2(x-100) & \mbox{ if } 100 < x \leq 1000 \\
1000 + .7(x-1000) & \mbox{ if } x > 1000 \\
\end{array}
\right.
\]
Where $C(x)$ is the cost in dollars for $x$ thousand gallons of water.
\begin{enumerate}
\item  What is $C(250)$?
\item  Write a sentence explaining what $C(250)$ means in terms of the water bill.
\end{enumerate}

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

\item  For the function $h$ below, find $f$ and $g$ so that $h(x)=f(g(x))$.
\[
h(x)=\frac{52}{\sqrt{5x^{4}-6x}}
\]

\item  For the function $f(x)=3x^2$, simplify the following:
\[
\frac{f(x+h)-f(x)}{h}
\]

\item  Lets say you are car shopping.  
You are dead set on a New Beetle.
Let say that Volkswagen sells the Beetle to Dave Strong (a VW dealer) and 20\% of that price
is VW's mark-up.
Then, on top of that, 35\% of the sticker price is Dave Strong's mark-up.
The Beetle costs VW \$9250.
Answer the following questions:
(As usual, I need to see the work for you to get credit.)
\begin{enumerate}
\item  What does Dave Strong pay VW for the New Beetle?
\item  What is the sticker price of the Beetle?
\end{enumerate}

\item  Graph the line $4x+5y=8$.
Find the coordinates of the $x$-intercept and the $y$-intercept and
label these points on your graph.




\end{enumerate}


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