Answer
$\displaystyle \lim_{\mathrm{x}\rightarrow-1}f(x)=1$
Work Step by Step
Follow the steps in "Evaluating Limits Graphically"
(steps 3-5: one-sided limits, limit at x=a)
x=-1
As we trace the graph on either side of x=$-1$ (but not $-1$ itself),
the points on the graph approach the point $(-1,1),$
f(x) approaches $-1$ (from either side), so
both one-sided limits exist and equal 1,
the limit $\displaystyle \lim_{\mathrm{x}\rightarrow-1}f(x)$ exists, and
$\displaystyle \lim_{\mathrm{x}\rightarrow-1}f(x)=1$