Answer
$f(x)$ is discontinuous at $x_{2} ,x_{4}$.
Work Step by Step
From the graph we find that:
$f(x)$ is discontinuous at $x_{2}$, since $f(x_{2})$ does not exist .
and also $ f(x)$ is discontinuous at $x_{4}$, since
$$
\lim\limits_{x \to x_{4}^{-}} f(x) \neq \lim\limits_{x \to x_{4}^{+}}
f(x).
$$
Therefore , $f(x)$ is discontinuous at $x_{2} ,x_{4}$.
