Answer
$ f(x) $ is left continuous at $ x=2$. Jump discontinuity at $x=2$.
Work Step by Step
One can see that
$\lim _{x \rightarrow 2^-} f(x)=-1=f(2)$
$\lim _{x \rightarrow 2^+} f(x)=1\neq f(2)$
Hence, $f(x)$ has a jump discontinuity at $x=2$ and is left continuous at $ x=2$.
