Let $f(x)=\{\begin{array}{cc}3-x,& x<mn>2</mn>\\ \frac{3x}{4}+1,& x>2\end{array}$

Complete parts a through $d$ below.

$($Simpility your answers.$)$

D$.\underset{x{2}^{+}}{lim}f(x)$ and $\underset{x{2}^{-}}{lim}f(x)$ do not exist.

b$.$ Does $\underset{x2}{lim}f(x)$ exist? If so$,$ what is it$?$ If not, why not? Select the correct choice below and, if necessary, fill in any answer box in your choice.

A$.$ Yes, $\underset{x2}{lim}f(x)$ exists and equals $\frac{5}{2}.$

$($Simplify your answer.$)$

B$.$ No$,\underset{x2}{lim}f(x)$ does not exist because $f(2)$ is undefined.

C$.$ No$,\underset{x2}{lim}f(x)$ does not exist because $\underset{x{2}^{+}}{lim}f(x)\underset{x{2}^{-}}{lim}f(x).$