Answer
$\lim\limits_{x \to \ -1}f(x)=-1$
Work Step by Step
In order to obtain the limit of $\lim\limits_{x \to \ -1} f(x)$ we have to first look at both one-sided limits. We only have to consider the limits, not the value of $f(-1)$.
As we trace the graph, both of these aforementioned limits exist and they are equal:
$\lim\limits_{x \to \ -1^{+}}f(x)=-1$
$\lim\limits_{x \to \ -1^{-}}f(x)=-1$
Therefore the $\lim\limits_{x \to \ -1}f(x)$ exists and equals to $-1$.