For which x-values is the graph below discontinuous?

A continuous graph is in essence a graph that can be sketched without interruption. We see that the points where there are such discontinuities are at the edges of the intervals.
Hence, the correct answer is the 2nd.

We can also get this result, by considering the point 0. The function is a line there, so it has no discontinuity. Hence, the correct point should not contain 0. But all other 3 choices contain it.