Answer
$\lim\limits_{x \to -2^-}f(x) \neq f(-2)$
$\lim\limits_{x \to -2^+}f(x) \neq f(-2)$
$\lim\limits_{x \to 2^-}f(x) = f(2)$
$\lim\limits_{x \to 2^+}f(x) \neq f(2)$
Work Step by Step
$\lim\limits_{x \to -2^-}f(x) \neq f(-2)$
As $x$ approaches $-2$ from the left side, the value of the function does not approach $f(-2)$. Therefore, the function is not left continuous at $x=-2$.
$\lim\limits_{x \to -2^+}f(x) \neq f(-2)$
As $x$ approaches $-2$ from the right side, the value of the function does not approach $f(-2)$. Therefore, the function is not right continuous at $x=-2$.
$\lim\limits_{x \to 2^-}f(x) = f(2)$
As $x$ approaches $2$ from the left side, the value of the function approaches $f(2)$. Therefore, the function is continuous from the left at $x=2$.
$\lim\limits_{x \to 2^+}f(x) \neq f(2)$
However, as $x$ approaches $2$ from the right side, the value of the function does not approach $f(2)$. Therefore, the function is not continuous from the right at $x=2$
