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\textbf{\LARGE{Math 111}}\\
\textbf{ Final}\\
For the entire test, let\\
 $f(x)=x^2+x-2$\\
and $g(x)=\frac{x^2-x-6}{x^2-x-2}$\\
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1.) Graph f(x)\vspace{5in}\\

2.) What's the domain of f(x)?\vspace{.2in}\\

3.) Looking at this function, what's it's range?\vspace{.2in}\\

4.) Is it linear? Quadratic?\pagebreak\\

1.) Graph g(x)\vspace{5in}\\

2.) What's the domain of g(x)?\vspace{.2in}\\

3.) Looking at this function, what's it's range?\vspace{.2in}\\

4.) Is it linear? Quadratic?\pagebreak\\

\textbf{\large{Part II}}\vspace{.5in}\\

Complete the following input/output charts.\\
\begin{tabbing}
$f(x)$\hspace{1in}\=$g(x)$\hspace{1in}\=$g\circ f(x)$\\
\underline{input output}\>\underline{input output}\>\underline{input output}\\
\vspace{.25in}\\
-3\>-2\>-3\\
\vspace{.25in}\\
-2\>-1\>-2\\
\vspace{.25in}\\
-1\>0\>-1\\
\vspace{.25in}\\
0\>1\>0\\
\vspace{.25in}\\
1\>2\>1\\
\vspace{.25in}\\
2\>4\>2\\

\end{tabbing}
\pagebreak

\textbf{\large{Part III}}\vspace{.2in}\\

1.) Evaluate $\frac{df(x)}{dx}$\vspace{3in}\\

2.) Find the equation of the line tangent to $f(x)$ at $x=1$.\vspace{3in}\\

3.) Graph the tangent line on the same graph as your graph of f(x) on p. 1\\
(hint: find b, the y-intercept, plot it, and connect it with (1, f(1))).\pagebreak


4.) Evaluate $\frac{dg(x)}{dx}$\vspace{3in}\\

5.) Find the equation of the line tangent to $g(x)$ at $x=1$.\vspace{3in}\\

6.) Graph the tangent line on the same graph as your graph of g(x) on p. 2\\
(hint: find b, the y-intercept, plot it, and connect it with (1, g(1))).\pagebreak

\textbf{\large{Part IV}}\vspace{.2in}\\

1.) Say you put 1250 in an account with .06 annual interest rate compounded monthly. How much will you have after 7 years? \vspace{3in}\\

2.) Say you have an account with .06 annual interest rate compounded monthly. How much do you need to put in your account now to have 2,000 in 5 years?\pagebreak


3.)Say you put 1250 in your account compounded continusouly at .06 annual interest rate. How much will be in your account after 7 years?\vspace{3in}\\

4.) Say you put 1250 in your account compounded continuously at .06 annual interest rate. How long until you have 2,000?\pagebreak

\textbf{\large{PartV}}\\
Evaluate the following derivatives:\vspace{.5in}\\

1.) $\frac{de^{(\frac{x^2-x-6}{x^2-x-2})}}{dx}$\vspace{3in}\\

2.) $\frac{dln{(x^2+x-2)}}{dx}$

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