Answer
$\displaystyle \lim_{x\rightarrow-1}f(x)=-\infty,\qquad\lim_{x\rightarrow 3}f(x)=+\infty$.
Work Step by Step
When x is slightly left of $-1$, approaching $-1,$
the graph falls without bound,
and when x is slightly right of $-1$ approaching $-1,$
it also falls without bound.
Neither of the one sided limits exist at $x=-1$
but both are $-\infty$, so we write
$\displaystyle \lim_{x\rightarrow-1}f(x)=-\infty$.
When x is slightly left of $3$, approaching $3,$
the graph rises without bound,
and when x is slightly right of $3$ approaching $3,$
it also rises without bound.
Neither of the one sided limits exist at $x=3$
but both are $+\infty$, so we write
$\displaystyle \lim_{x\rightarrow 3}f(x)=+\infty$.
