Analyze and sketch the graph of $f(x) = \frac{18}{x^2 - 9}$.
Be sure to include the following in your analysis: domain, range, $x$-intercepts, $y$-intercepts, vertical
asymptotes (if any), horizontal asymptotes (if any), symmetry (if any), end behavior, first derivative and
critical points, second derivative and possible inflection points, intervals where $f$ is increasing/decreasing,
intervals where $f$ is concave up/concave down, and any local extrema. Label the following on your sketch:
vertical asymptotes, horizontal asymptotes, local extrema (if any), $x$-intercepts, and $y$-intercepts.