Answer
not continuous
Work Step by Step
$f(x)$ will be continuous at $x=-2$ if $f(-2)=\lim_{x\to -2}f(x)$. We know that $f(-2)=4$.
$$\lim_{x\to -2}f(x)\\=\lim_{x\to -2}\frac{x^2-4}{x+2}\\=\lim_{x\to -2}\frac{(x+2)(x-2)}{(x+2)}\\=\lim_{x\to -2}(x-2)=(-2)-2=-4$$
$4\ne-4$, hence it is not continuous at $-2$.
