Answer
There is a discontinuity when $a=-2$.
The limit of this function does not exist.
Work Step by Step
We are given $p(x)=\frac{|x+2|}{x+2}$
This rational function is discontinuous wherever the denominator is zero.
There is a discontinuity when $a=-2$
For $x\lt-2 \rightarrow \frac{|x+2|}{x+2}=\frac{-(x+2)}{-(x+2)}=1$
For $x\gt-2 \rightarrow \frac{|x+2|}{x+2}=\frac{-(x+2)}{x+2}=-1$
Thus, the limit of this function does not exist