Answer
$f(x)$ has an irremovable jump discontinuity at $x=-7.$
Work Step by Step
The function is 0/0, and not defined at $x=-7.$
$\lim\limits_{x\to-7^+}f(x)=\dfrac{|-7^++7|}{-7^++7}=\dfrac{0^+}{0^+}=1.$
$\lim\limits_{x\to-7^-}f(x)=\dfrac{|-7^-+7|}{-7^-+7}=\dfrac{0^+}{0^-}=-1.$
Since $\lim\limits_{x\to-7^+}f(x)\ne\lim\limits_{x\to-7^-}f(x)$ then $\lim\limits_{x\to7}f(x)$ doesn't exist. and the function has a jump discontinuity.
