To determine where the function $g(x)$ is discontinuous based on the graph, we need to observe any breaks, jumps, or holes in the graph.

Discontinuities in the graph:

1. At $x = -2$: There is a jump discontinuity, as the graph jumps from one value to another.
2. At $x = 0$: The graph has a vertical asymptote, indicating a discontinuity at $x = 0$.
3. At $x = 1$: There is a removable discontinuity (hole), as the graph has a hollow circle at $x = 1$.

However, you missed one more discontinuity:

4. At $x = 3$: The graph also has a discontinuity at $x = 3$ since there is a break in the graph.

Correct list of discontinuities:

• $x = -2, 0, 1, 3$

Let me know if you'd like more details or have any questions!

Here are 5 related questions to explore further:

1. What types of discontinuities exist (removable, jump, infinite)?
2. How do we define continuity of a function at a point?
3. What conditions must be met for a function to be continuous at a point?
4. How can discontinuities affect the limits of a function?
5. How can graphing technology assist in identifying discontinuities?

Tip: Always check for breaks, jumps, and hollow circles when determining discontinuities from a graph.