Answer
We can see a sketch of a possible graph below.
Work Step by Step
$\lim\limits_{x \to -\infty}f(x) = -2$
The value of the function gets closer to $y = -2$ as $x$ gets more and more negative.
$\lim\limits_{x \to \infty}f(x) = 0$
The value of the function gets closer to $y = 0$ as $x$ gets more and more positive.
$\lim\limits_{x \to -3}f(x) = \infty$
The value of the function gets more and more positive as $x$ gets closer to $x=-3$
$\lim\limits_{x \to 3^-}f(x) = -\infty$
The value of the function gets more and more negative as $x$ gets closer to $x=3$ from the left side.
$\lim\limits_{x \to 3^+}f(x) = 2$
The value of the function gets closer to $y = 2$ as $x$ gets closer to $x=3$ from the right side.
$f$ is continuous from the right at $3$
$f(3) = 2$
We can see a sketch of a possible graph below.
