Answer
Since the function is not right continuous at $ x = -1$, the function is not continuous at $x = -1$
Work Step by Step
$f(-1) = (-1)+3 = 2$
$\lim\limits_{x \to -1^-}f(x) = (-1)+3 = 2 = f(-1)$
As $x$ approaches $-1$ from the left side, the value of the function approaches $f(-1)$. Therefore, the function is left continuous at $x=-1$.
$\lim\limits_{x \to -1^+}f(x) = 2^{-1} = \frac{1}{2} \neq f(-1)$
As $x$ approaches $-1$ from the right side, the value of the function does not approach $f(-1)$. Therefore, the function is not right continuous at $x=-1$.
Since the function is not right continuous at $ x = -1$, the function is not continuous at $x = -1$
