The graph depicts the function $f(x)$ and asks for the $x$-values where the function is not continuous.

To find where $f(x)$ is not continuous, we look for discontinuities such as jumps, holes (removable discontinuities), or vertical asymptotes.

Points of discontinuity:

1. At $x = -2$: There is an open circle on the graph, indicating a hole, meaning $f(x)$ is not continuous here.

2. At $x = -1$: A vertical asymptote is present at $x = -1$, implying a discontinuity.

3. At $x = 0$: The graph has an open circle at $x = 0$ and no connected value, meaning a discontinuity at this point as well.

4. At $x = 1$: There's no indication of discontinuity. The function is continuous at this point.

5. At $x = 2$: An open circle is seen at $x = 2$, implying another discontinuity.

6. At $x = 4$: No discontinuity is observed here, as the function appears continuous.

Conclusion:

The function is not continuous at the following $x$-values:

• $x = -2$
• $x = -1$
• $x = 0$
• $x = 2$

Therefore, the correct answers are:

• $x = -2$
• $x = -1$
• $x = 0$
• $x = 2$

Would you like more details or further explanations?

Here are 5 related questions:

1. What are the types of discontinuities in a function?
2. How can we determine whether a function is continuous at a specific point?
3. What is the difference between a removable discontinuity and a jump discontinuity?
4. How do vertical asymptotes affect the continuity of a function?
5. Can a function have discontinuities and still be differentiable elsewhere?

Tip: A function is continuous at a point $x = a$ if $\lim_{x \to a} f(x) = f(a)$.