For the function $f$ whose graph is given, state the value of the given quantity if it exists. $($If an answer does not exist, enter DNE.$)$

$($a$)\underset{x{4}^{-}}{lim}f(x)$

$$

$($b$)\underset{x{4}^{+}}{lim}f(x)$

$$

$($c$)\underset{x4}{lim}f(x)$

$$

$($d$)\underset{x20}{lim}f(x)$

$($e$)f(20)$