Answer
(a) $a=5$
(b) $a=1,3,5$
(c) $a=1,3$
Work Step by Step
From the graph, $f$ has an infinite discontinuity at $x=1$ ($\lim_{x\to 1}f(x)=\infty$), a removable discontinuity at $x=3$, and a jump discontinuity at $x=5$.
Thus,
(a) $\lim_{x\to a}f(x)$ does not exist at $a=5$;
(b) $f$ is not continuous at $a=1,3,5$;
(c) $\lim_{x\to a}f(x)$ exists but $f$ is not continuous at $a=1,3$.
