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Problems PreCal 1508 Review, September 21, 2011 \\
PL: Alex Knaust, Lecturer: Yi-Yu Liao
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\begin{enumerate}
\item Find the \emph{slope-intercept form} of the equation of the line passing through the two points $(1, -2), (2, -3)$.

\item Find the \emph{slope-intercept form} of the equation of a line passing through the point $(-9, 9)$ and perpendicular to line $y = 3x - 2$

\item Determine the implied domain for the following functions
\begin{enumerate}
\item $f(x) = x^3 + 2x + 9$
\item $h(x) = \frac{2x}{\sqrt{x - 3}}$
\item $q(x) = \frac{9}{x^2 - 9}$
\end{enumerate}

\item For the following functions find $f \circ g$, $f - g$, $\frac{f}{g}$
\begin{enumerate}
\item $f(x) = 3x - 9,\quad g(x) = x^2 + 7$
\item $f(x) = \sqrt{x - 1},\quad g(x) = x^4 + 2$
\end{enumerate}

\item Find the vertex and the x-intercepts of the following quadratic functions
\begin{enumerate}
\item $f(x) = x^2 - 9x + 2$
\item $f(x) = 4x - 1 - 4x^2$
\end{enumerate}

\item Find the inverse function (if it exists) of the following functions
\begin{enumerate}
\item $f(x) = \frac{2}{\sqrt{x}}$
\item $h(x) = (x - 2)^2 - 9$
\end{enumerate}

\item Find all zeros of the functions (Real and Imaginary)
\begin{enumerate}
\item $f(x) = x^2 + 1$
\item $f(x) = x^2 + x + 2$
\item $f(x) = 2x^4 - 6x^3 - 4x^2 + 20x - 24,\quad \text{given  } f(1 + i) = 0$
\end{enumerate}

\item Write $f(x)$ as $f(x) = q(x)d(x) + r(x)$ (Division Theorem)
\begin{enumerate}
\item $f(x) = x^3 + 2x + 9,\quad d(x) = x -3$
\item $f(x) = x^5 + 3x^4 + 9x + 2, \quad d(x) = x + 2$
\end{enumerate}

\item Determine if $-3$ is a root of $f(x) = 2x^4 - 6x^3 - 38x^2 + 54x + 180$ (use synethetic division)

\item Write the definitions of the following
\begin{enumerate}
\item The inverse function of $f$
\item A polynomial
\item Root of a function
\item Rational Function
\end{enumerate}
\end{enumerate}
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(Select) Solutions to the problems will be available at \url{http://rylai.dyndns.org/review\_1.pdf}\\
You can reach me via e-mail at \url{awknaust@miners.utep.edu}\\
I expect you all to do well on the exam! Good Luck!
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