$Is$ the given function continuous $at$ the given values $ofx?$

$f(x)=\{\begin{array}{ccc}x-2& if& x4\\ [2-x& if& x>4]\text{;}x=2\\ x=4\end{array}$

$Is$ the function continuous $atx=2?$ Select the correct choice below and, $if$ necessary, fill $in$ the answer box $to$ complete your choice.

$A.$ Yes, the point $is$ defined, $\underset{x2}{lim}f(x)$ exists, and $\underset{x2}{lim}f(x)=(Simplify$ your answer.$)$

$B.No,$ the function $is$ not continuous $atx=2.$