Question

which of the following graphs show a jump discontinuity? (select all that apply)

Explanation:

Step1: Recall jump - discontinuity definition

A jump discontinuity occurs when the left - hand limit and the right - hand limit of a function at a point exist but are not equal.

Step2: Analyze first graph

The first graph has a vertical asymptote. It is an infinite discontinuity, not a jump discontinuity.

Step3: Analyze second graph

The second graph has a removable discontinuity (a hole). The left - hand and right - hand limits are equal at the point of the hole, so it is not a jump discontinuity.

Step4: Analyze third graph

In the third graph, as we approach the point from the left and from the right, the function approaches different values. The left - hand limit and the right - hand limit exist and are not equal, so it has a jump discontinuity.

Answer:

The third graph shows a jump discontinuity.