Answer
a) -4, $f(-4)$ is not defined.
-2, the left and right hand limits are not equa,l so the limit does not exist.
2, the left and right hand limits are not equal, so the limit does not exist.
4, the left and right hand limits are not equal, so the limit does not exist.
b) -4, neither
-2, left
2, right
4, right
Work Step by Step
a) Since $f$ is not defined at $x = -4$, $f$ is not continuous from any side at $x = -4$.
$f$ is not continuous at $x=2$ and at $x=4$.
b) $f(-2) = \lim\limits_{x \to -2^-}f(x)$, so $f$ is continuous from the left.
$f(2) = \lim\limits_{x \to 2^+}f(x)$, so $f$ is continuous from the right.
$f(4) = \lim\limits_{x \to 4^+}f(x)$, so $f$ is continuous from the right.
