Calculus with Applications (10th Edition)

There is a discontinuity when $a=-2$. The limit of this function does not exist.
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