Chapter 1.5, Problem 1ES

Let $f$ be the function whose graph is shown. On which of the following intervals, if any, is $f$ continuous?

(a) $\left[1,3\right]$

(b) $\left(1,3\right)$

(c) $\left[1,2\right]$

(d) $\left(1,2\right)$

(e) $\left[2,3\right]$

(f) $\left(2,3\right)$

For each interval on which $f$ is not continuous, indicate which conditions for the continuity of $f$ do not hold.