$9.$ Sketch a graph of the function: $\backslash ($ y$=\backslash$frac$\{$x$^\{2\}-3\}\{$x$-2\}\backslash ).$ Use derivatives to justify your graph; where increasing, decreasing, asymptotes, etc.; A copy of a graph from a graphing calculator will not be accepted.

$(10$ Points$)$

$($Hint: must use infinite limits and limits at infinity$)$