For each function $f$ graphed in Exercises $23-26,$ describe the intervals on which $f$ is continuous. For each discontinuity of $f,$ describe the type of discontinuity and any one$-$sided continuity. Justify your answers about discontinuities with limit statements.

$2$

$2$

Sketch the graph of a function $f$ described in Exercises $27-32,$ if possible. If it is not possible, explain why not.

$28.f$ is left continuous at $x=2$ but not continuous at $x=2,$ and $f(2)=3.$