The graph you provided represents the function $g(x)$, and the task asks to identify the points where the function is discontinuous.

From the graph, discontinuities occur when the function is either undefined, has breaks, jumps, or holes.

Observing the graph, I can see discontinuities at:

1. $x = -2$: There is a break, indicating a jump discontinuity.
2. $x = 0$: There is a hole in the graph, indicating a removable discontinuity.
3. $x = 1$: There is a hole followed by a jump, indicating both a removable discontinuity and a jump discontinuity.

Thus, the function is discontinuous at $x = -2, 0, 1$.

Would you like more details on each type of discontinuity?

Relative Questions:

1. What are the differences between a removable and a jump discontinuity?
2. How does the concept of limits relate to discontinuities in functions?
3. Can a function be discontinuous at an asymptote? Why or why not?
4. What conditions make a function continuous at a point?
5. How would you graphically determine if a function has an infinite discontinuity?

Tip:

When analyzing discontinuities, check if the function has a hole, jump, or vertical asymptote, as these usually signal points of discontinuity.