Answer
a) $a=1$
b) $a=1,3$
c) $a=3$
Work Step by Step
From the graph, $f$ has a jump discontinuity at $x=1$ and a removable discontinuity at $x=3$.
Thus,
(a) $\lim_{x\to a}f(x)$ does not exist at $a=1$;
(b) $f$ is not continuous at $a=1,3$;
(c) $\lim_{x\to a}f(x)$ exists but $f$ is not continuous at $a=3$.
