Answer
The function $f(x)$ is not continuous at $c=-2$.
Work Step by Step
We are given:
$f(x)=\dfrac{x^2-4}{x+2}$
We need to determine if $f(x)$ is continuous at $c=-2$.
We check the left-hand and right-hand limits. If they are equal to each other and the value of the function at the limit, then the function is continuous at that point.
$\lim\limits_{x \to 2^{-}}f(x)=\lim\limits_{x \to 2^{-}}\dfrac{x^2-4}{x+2} \\=\dfrac{(-2)^2-4}{-2+2} \\=\dfrac{0}{0}$
We got an undefined value, so the function cannot be defined at $c=-2$.
Therefore, the function $f(x)$ is not continuous at $c=-2$.
