Answer
$$\begin{align*}
\lim _{x \rightarrow 1^-} f(x) =3 \\
\lim _{x \rightarrow 1^+} f(x) =3\\
\lim _{x \rightarrow 3^-} f(x) =-\infty \\
\lim _{x \rightarrow 3^+} f(x) =4\\
\lim _{x \rightarrow 5-} f(x) =2 \\
\lim _{x \rightarrow 5+} f(x) =-3 \\
\lim _{x \rightarrow 6-} f(x) =\infty\\
\lim _{x \rightarrow 6+} f(x) =\infty
\end{align*}$$
Work Step by Step
We observe the left and right limits at the points $c=1,3,5,6$ by looking at the given graph:
\begin{align*}
\lim _{x \rightarrow 1^-} f(x)&=3\\
\lim _{x \rightarrow 1^+} f(x)&=3\\
\lim _{x \rightarrow 3^-} f(x)&=-\infty \\
\lim _{x \rightarrow 3^-} f(x)&=4\\
\lim _{x \rightarrow 5-} f(x)&=2 \\
\lim _{x \rightarrow 5+} f(x)&=-3 \\
\lim _{x \rightarrow 6-} f(x)&=\infty\\
\lim _{x \rightarrow 6+} f(x)&=\infty
\end{align*}
