Answer
$ a.\quad -\infty$.
$ b.\quad -\infty$.
$ c.\quad -\infty$
$ d.\quad -\infty$
$ e.\quad -\infty$.
$ f.\quad -\infty$
Work Step by Step
$ a.\quad$
Nearing $x=-2$ from the left, the graph falls without bound. $\displaystyle \lim_{x\rightarrow-2^{-}}p(x)=-\infty$.
$ b.\quad$
Nearing $x=-2$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow-2^{+}}p(x)=-\infty$.
$ c.\quad$
Neither one-sided limit exists, but both are $-\infty.$
We write: $\displaystyle \lim_{x\rightarrow-2}p(x)=-\infty$.
$ d.\quad$
Nearing $x=3$ from the left, the graph falls without bound. $\displaystyle \lim_{x\rightarrow 3^{-}}p(x)=-\infty$.
$ e.\quad$
Nearing $x=3$ from the right, the graph falls without bound. $\displaystyle \lim_{x\rightarrow 3^{+}}p(x)=-\infty$.
$ f.\quad$
Neither one-sided limit exists, but both are $-\infty.$
We write: $\displaystyle \lim_{x\rightarrow 3}p(x)=-\infty$.
