Answer
From the graph we find that:
(a)
$$
\lim\limits_{x \to 4^{-}} f(x)=\infty
$$
(b)
$$
\lim\limits_{x \to 4^{+}} f(x)=-\infty
$$
(c)
$$
\lim\limits_{x \to 4} f(x)
$$
does not exist since,
$$
\lim\limits_{x \to 4^{-}} f(x)=\infty \neq \lim\limits_{x \to 4^{+}} g(x)=-\infty
$$
(d)
From the graph we find that:
$$
f(4)
$$
does not exist since the graph has no point with an $x$-value of 4.
Notice in the figure that at a point 4 where the function is
discontinuous.
Work Step by Step
From the graph we find that:
(a)
$$
\lim\limits_{x \to 4^{-}} f(x)=\infty
$$
(b)
$$
\lim\limits_{x \to 4^{+}} f(x)=-\infty
$$
(c)
$$
\lim\limits_{x \to 4} f(x)
$$
does not exist since,
$$
\lim\limits_{x \to 4^{-}} f(x)=\infty \neq \lim\limits_{x \to 4^{+}} g(x)=-\infty
$$
(d)
From the graph we find that:
$$
f(4)
$$
does not exist since the graph has no point with an $x$-value of 4.
Notice in the figure that at a point 4 where the function is
discontinuous.