Which of the following accurately lists all the discontinuities for the graph below

The correct answer is option B.

From the graph we can see the following discontinuities:
a) A hole at x = -2
b) A jump at x = 0
c) A hole at x = 8

The hole refers to the point discontinuity and the jump refers to as jump discontinuity. The function is defined and is continuous at x = 3

Thus, the given graph has jump discontinuity  at x = 0 and point discontinuity at x = -2 and x = 8