Suppose that

$\backslash [$

f$($x$)=\backslash$frac$\{3$ x$\}\{$x$^\{2\}-16\}$

$\backslash ]$

$($A$)$ List all critical numbers of $\backslash ($ f $\backslash ).$ If there are no critical numbers, enter 'NONE'.

Critical numbers $\backslash (=\backslash )$

$($B$)$ Use interval notation to indicate where $\backslash ($ f$($x$)\backslash )$ is decreasing.

Note: Use 'INF' for $\backslash (\backslash$infty $\backslash ),\text{'}-$INF' for $\backslash (-\backslash$infty $\backslash ),$ and use $\text{'}$U$\text{'}$ for the union symbol.

Decreasing:

$($C$)$List the $\backslash ($ x $\backslash )-$values of all local maxima of $\backslash ($ f $\backslash ).$ If there are no local maxima, enter 'NONE'.

$\backslash ($ x $\backslash )$ values of local maxima $\backslash (=\backslash )$

$($D$)$ List the $\backslash ($ x $\backslash )-$values of all local minima of $\backslash ($ f $\backslash ).$ If there are no local minima, enter 'NONE'.

$\backslash ($ x $\backslash )$ values of local minima $\backslash (=\backslash )$

$($E$)$ List the $\backslash ($ x $\backslash )$ values of all inflection points of $\backslash ($ f $\backslash ).$ If there are no inflection points, enter 'NONE'.

Inflection points $=$

$($F$)$ Use interval notation to indicate where $\backslash ($ f$($x$)\backslash )$ is concave up$.$

Concave up:

$($G$)$ Use interval notation to indicate where $\backslash ($ f$($x$)\backslash )$ is concave down.

Concave down:

$($H$)$ List all horizontal asymptotes of $\backslash ($ f $\backslash ).$ If there are no horizontal asymptotes, enter 'NONE'.

Horizontal asymptotes $\backslash ($ y$=\backslash )$

$($I$)$ List all vertical asymptotes of $\backslash ($ f $\backslash ).$

If there are no vertical asymptotes, enter 'NONE'.

vertical asymptotes $\backslash ($ x$=\backslash )$

$($J$)$ Use all of the preceding information to sketch a graph of $\backslash ($ f $\backslash ).$ When you're finished, enter a $"1"$ in the box below.

Graph Complete: