$($A$)$ Find the limit $\underset{?}{lim}f(x).$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

$x-1^{+}$

A$.\underset{x-1^{+}}{lim}f(x)=4($Type an integer.$)$

B$.$ The limit does not exist.

$($B$)$ Find the limit $\underset{x-1^{-}}{lim}f(x).$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.($Type an integer.$)$

B$.$ The limit does not exist.

$($C$)$ Find the limit $\underset{x-1}{lim}f(x).$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.\underset{x-1}{lim}f(x)=($Type an integer.$)$

$$

B$.$ The limit does not exist,

$($D$)$ Find the function value $f(-1).$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.f(-1)=-2($Type an integer.$)$

B$.$ The function is not defined at $x=-1.$