For the function $g$ whose graph is given, state the following. $($If the limit is infinite, enter $\text{'}\text{'}$ or $\text{'}-\text{'},$ as appropriate. If the limit does not otherwise exist, enter DNE.$)$

$$

$(1)$

$($a$)\underset{x}{lim}g(x)$

$$

$($b$)\underset{x-}{lim}g(x)$

$($c$)\underset{x3}{lim}g(x)$

$$

$($d$)\underset{x0}{lim}g(x)$

$($e$)\underset{x-2^{+}}{lim}g(x)$