Answer
Limit Does Not Exist
Work Step by Step
We need to build a table that shows the values of $x$ close to $-4$ from the left and right sides and the values of $f(x)$ for those values of $x$.
From the graph, we see that the two limits do not match.
$\lim_\limits {x \to -4}f(x)=$ Limit Does Not Exist