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\newcommand{\bfrac}[2]{\displaystyle \frac{#1}{#2}}
\newcommand{\limit}[2]{\displaystyle \lim_{{#1} \rightarrow {#2}}} 

\begin{document}
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%**********************TITLE PAGE*********************************
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\begin{large}

{\bf Name:}      
\underline{$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$}\\

{\bf Student Identification Number:}      
\underline{$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$}\\

{\bf TA's Name:} \underline{$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$}\\
\vspace{1cm}

\begin{center}
{\bf Calculus I\\
SKILLS TEST I} \\
Practice Test\\
\end{center}

\end{large}
\vspace{3cm}

{\bf Directions:} You have two hours to complete this test. READ ALL  
DIRECTIONS CAREFULLY!   Partial credit will be given, but ONLY IF YOU  
SHOW YOUR WORK! \\
\vspace{2cm}

\noindent
Unless otherwise specified, you may assume that each problem is worth 5 points.  
Please indicate ALL answers clearly by drawing a box around the final answer.\\

\newpage

\begin{enumerate}

\item   (2 points each) {\bf TRUE OR FALSE:}  For each of the following, indicate whether the statement is true or false.

\begin{enumerate}
\item   \underline{$~~~~~~~~~~~~~$} $\sqrt[3]{x^3}=|x|$

\item   \underline{$~~~~~~~~~~~~~$} $\ln{(A^n+B)}=n \ln{A} + \ln{B}$

\item   \underline{$~~~~~~~~~~~~~$} $\cos{(2x)}=1-2 \, \mbox{sin}^2(x)$

\item   \underline{$~~~~~~~~~~~~~$} Any rational function has a domain of all real numbers.\\

\item   \underline{$~~~~~~~~~~~~~$} If $f(x)$ is a polynomial such that $f(a)=0,$ then $x-a$ is a factor of $f(x).$\\
\end{enumerate}

\item   What is the {\bf Domain} of $f(x)=tan(x).$
\vspace{3cm}

\item   What is the {\bf Range} of the function $f(x)=x^2 - 4.$
\vspace{3cm}

\item   Which of the following functions has a {\bf Range} which is equal to its {\bf Domain}?

\begin{enumerate}

\item   $f(x)=\frac{1}{x^2}$

\item   $f(x)=\sin{x}$

\item   $f(x)=\frac{1}{x}$

\item   $f(x)=5$

\item   None of the above\\

\end{enumerate}


\item   Do the lines given by the equations $7y+3x-17=0$ and $3y-2x+15=0$ ever intersect?  If so, where?  If not, why not?
\vspace{4cm}

\item   Find the equation of the line whose $x$-intercept is 10 and whose $y$-intercept is 5.
\vspace{3cm}

\item   Which of the following functions is {\bf even}?

\begin{enumerate}

\item   $f(x)=\sin{x}$

\item   $f(x)=\bfrac{\sin^2(x)}{\cos(x)}$

\item   $f(x)=\bfrac{1}{x}$

\item   $f(x)=\ln{(x^2-2)}$

\item   None of the above\\

\end{enumerate}


\item   (2 pts each)  Given that $\ln{A}=f,$ $\ln{B}=g,$ and $\ln{C}=h,$ evaluate the following expressions in terms of $f,~g,$ and $h.$

\begin{enumerate}

\item   $\ln{(ABC)}$
\vspace{2cm}

\item   $\ln{((AB)^2)}$
\vspace{2cm}

\item   $\ln{(\bfrac{1}{\sqrt{C}})}$
\vspace{2cm}

\end{enumerate}

\item   If $f(g(x))=(x^2+4x+4) + 2x + 4$ and $g(x)=x+2$, what is $f(x)$?

\begin{enumerate}

\item   $f(x)=(x^2+4x+4) + 2x + 2$

\item   $f(x)=x^2+4$

\item   $f(x)=x^2+2x$

\item   $f(x)=(x+2)+2$

\item   None of the above\\

\end{enumerate}
\newpage

\item   If $h(x)=\sqrt{x}$, $k(x)=x^2,$ and $l(x)=x+1$, what composition of the functions $h,~k$ and $l$ would give us $|x+1|$?
\vspace{3cm}

\item   Given the graph of {\bf any} function $f(x)$, which of the following choices would produce a graph that is identical in shape to $f(x)$ but that is moved 2 units up and 2 units to the left?

\begin{enumerate}

\item   $f(x)+2$

\item   $f(x)-2$

\item   $f(x+2)+2$

\item   $f(x-2)+2$

\item   None of the above\\

\end{enumerate}

\item Find the following limits. \\
\begin{enumerate}
\item $\limit{x}{2} \bfrac{x^{2}-4}{x-2}$ \\
\vspace{.5in}

\item $\limit{x}{2} \bfrac{x^{2}-4}{x^{2} + 8}$ \\
\vspace{.5in}

\item $\limit{x}{0} \bfrac{\sin(x)}{\cos(x)}$ \\
\vspace{.5in}

\item $\limit{x}{0} 12\pi$ \\
\vspace{.5in}
\end{enumerate}


\item   Find all points where the graphs of the functions $f(x)=x^2+2$ and $g(x)=2x+1$ intersect.\\
\vspace{4cm}
\newpage

\item (2 points each)  From their general shapes match each of the 
following functions with one of the graphs.  Write down the color
of the correct graph.

~~~~~~~~~~~The Basics:

\begin{enumerate}

\item \underline{$~~~~~~~~~~~~~$}   $f(x) = x^3$\\
\item \underline{$~~~~~~~~~~~~~$}   $f(x) = \sin(x)$\\
\item \underline{$~~~~~~~~~~~~~$}   $f(x) = \bfrac{1}{x} $\\
\item \underline{$~~~~~~~~~~~~~$}   $f(x) = |x| $\\

\end{enumerate}

\includegraphics[height=5in,width=4in,angle=-90]{funcs.eps}

\end{enumerate}
\end{document}
