\documentstyle[12pt,fleqn]{article}
\pagestyle{empty}
\setlength{\topmargin}{-1in}
\setlength{\oddsidemargin}{-.3in}
\setlength{\textheight}{9in}
\setlength{\textwidth}{7.2in}

\begin{document}


\begin{center}
{\Large Math 105 - 4}

Test 1
\end{center}
\vspace{.3in}

Show all work.  Use the back of the test pages if necessary.  Make your work neat.
\vspace{.3in}
\begin{enumerate}

\item  Name \rule{5.in}{.3pt}

\item (5 points) Find the equation of the line passing through the points: $(3,-14)$ and $(-3,4)$.  Put your answer in slope intercept form.
\vspace{2in}

\item (5 points)  Is this a graph of a function of $x$?  Why or why not?

\vspace{.1in}

\setlength{\unitlength}{1.5pt}
\begin{picture}(100,100)
\put(0,50){\vector(1,0){100}}
\put(50,0){\vector(0,1){100}}
\put(95,53){$x$}
\put(53,95){$y$}
\end{picture}
\vspace{.1in}

\item (10 points)  If $f(x)=\sqrt{2x-3}$ and $g(x)=x-5$, what is the domain of
$\frac{f}{g}(x)$?
%\vspace{2.3in}
\newpage

\item  
\begin{enumerate}
\item  (5 points)  What condition does a function have to satisfy in order to have an inverse?
\vspace{1in}
\item  (5 points)  Does the function $g$ below satisfy the condition?  If not tell me why not, if $g$ does, find the inverse of $g$.
\[
g(x)=\frac{4-x}{2-3x}
\]
\end{enumerate}
\vspace{2.3in}
%\newpage

\item (10 points)  Graph the inequality:
\[
\frac{-x+8}{x-5} \leq 0
\]
%\vspace{2.3in}
\newpage

\item (15 points)  Factor completely:
\[
x^3-x^2+2x+4
\]
\vspace{2.8in}
%\newpage

\item (5 points)  If $i$ is a zero of : $f(x)=x^4-2x^3+11x^2-2x+10$ find one other zero.
%\newpage
\vspace{1.8in}

\item  (15 points)  Isaac Newton is watching Keith Van Horn play a game of basket ball.  Isaac computes the trajectory of the ball when Keith makes a basket.  It turns out that the equation of the height, $y$, of the ball (above the floor of the court) is given by the equation below where x is the distance of the ball from Keith.
\[
y=-\frac{1}{5}x^2+2x+10
\]
How high does the ball get above the floor?
%\vspace{3in}
\newpage

\item  (25 points)  Graph $f(x)$ and find the items below.
\[
f(x)=\frac{2x^2}{x^2-4}
\]
\begin{enumerate}
\item  (3 point)  y-intercept(s):
\vspace{.2in}
\item  (3 points)  x-intercept(s):
\vspace{.2in}
\item  (3 points) Vertical asymptote(s):
\vspace{.2in}
\item  (3 points)  Horizontal asymptote(s):
\vspace{.2in}
\item  (2 points)  Slant asymptote(s):
\vspace{.2in}
\item  (2 points)  What happens to $f(x)$ as $x\rightarrow \infty$?
\vspace{.2in}
\item  (2 points)  What happens to $f(x)$ as $x\rightarrow -\infty$?
\vspace{.2in}
\end{enumerate}

\setlength{\unitlength}{3pt}
\begin{picture}(100,100)
\put(0,50){\vector(1,0){100}}
\put(50,0){\vector(0,1){100}}
\put(95,53){$x$}
\put(53,95){$y$}
\end{picture}
%\newpage


\end{enumerate}

\end{document}






