Answer
From the graph we find that:
(a)
$$
\lim\limits_{x \to -1^{-}} g(x)=-2
$$
(b)
$$
\lim\limits_{x \to -1^{+}} g(x)=2
$$
(c)
$$
\lim\limits_{x \to -1} g(x)
$$
does not exist since,
$$
\lim\limits_{x \to -1^{-}} g(x)=-2 \neq \lim\limits_{x \to -1^{+}} g(x)=2
$$
(d)
From the graph we find that:
$$
f(-1)=-2
$$
since the point $(-1,-2)$ is a point of the graph $g(x).$
Work Step by Step
From the graph we find that:
(a)
$$
\lim\limits_{x \to -1^{-}} g(x)=-2
$$
(b)
$$
\lim\limits_{x \to -1^{+}} g(x)=2
$$
(c)
$$
\lim\limits_{x \to -1} g(x)
$$
does not exist since,
$$
\lim\limits_{x \to -1^{-}} g(x)=-2 \neq \lim\limits_{x \to -1^{+}} g(x)=2
$$
(d)
From the graph we find that:
$$
f(-1)=-2
$$
since the point $(-1,-2)$ is a point of the graph $g(x).$