Answer
$ a.\quad -\infty$.
$ b.\quad -\infty$.
$ c.\quad -\infty$
$ d.\quad \infty$.
$ e.\quad -\infty$.
$ f.\quad$ does not exist.
Work Step by Step
$ a.\quad$
Nearing $x=-2$ from the left, the graph falls without bound. $\displaystyle \lim_{x\rightarrow-2^{-}}h(x)=-\infty$.
$ b.\quad$
Nearing $x=-2$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow-2^{+}}h(x)=-\infty$.
$ c.\quad$
Neither one-sided limit exists, but both are $-\infty.$
We write: $\displaystyle \lim_{x\rightarrow-2}h(x)=-\infty$.
$ d.\quad$
Nearing $x=3$ from the left, the graph rises without bound. $\displaystyle \lim_{x\rightarrow 3^{-}}h(x)=\infty$.
$ e.\quad$
Nearing $x=3$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow 3^{+}}h(x)=-\infty$.
$ f.\quad$
Neither one-sided limit exists, one is $+\infty$, the other $-\infty.$
We write: $\displaystyle \lim_{x\rightarrow 3}h(x)$ does not exist.
