Answer
$\lim\limits_{x \to -1^-}f(x) = f(-1)$
$\lim\limits_{x \to -1^+}f(x) \neq f(-1)$
$\lim\limits_{x \to 4^+}f(x) = f(4)$
$\lim\limits_{x \to 4^-}f(x) \neq f(4)$
Work Step by Step
$\lim\limits_{x \to -1^-}f(x) = f(-1)$
As $x$ approaches $-1$ from the left side, the value of the function approaches $f(-1)$. Therefore, the function is continuous from the left at $x=-1$.
$\lim\limits_{x \to -1^+}f(x) \neq f(-1)$
However, as $x$ approaches $-1$ from the right side, the value of the function does not approach $f(-1)$. Therefore, the function is discontinuous at $x=-1$
$\lim\limits_{x \to 4^+}f(x) = f(4)$
As $x$ approaches $4$ from the right side, the value of the function approaches $f(4)$. Therefore, the function is continuous from the right at $x=4$.
$\lim\limits_{x \to 4^-}f(x) \neq f(4)$
However, as $x$ approaches $4$ from the left side, the value of the function does not approach $f(4)$. Therefore, the function is discontinuous at $x=4$
