https://file.aiquickdraw.com/mathbot/file/17264407272848iqfvpdu.jpg

From the graph you uploaded, you are being asked to determine the discontinuities in the function \( f(x) \) at various \( x \)-values. For each discontinuity, you need to classify the type of continuity:

1. **Continuous from the left**: The function approaches the same value from the left as it is at the point.
2. **Continuous from the right**: The function approaches the same value from the right as it is at the point.
3. **Neither**: The function is discontinuous from both directions (left and right).

### Let's analyze the points of discontinuity:

1. **At \( x = -4 \)**: The function has an open circle, meaning that it does not have a value at \( x = -4 \), and there is no continuity from either the left or the right. This is a **discontinuity where neither side is continuous**.

2. **At \( x = -2 \)**: The graph has a filled point on the left and an open circle on the right. This suggests that the function is **continuous from the left**, but not from the right.

3. **At \( x = 0 \)**: There is no apparent discontinuity at \( x = 0 \), so the function is continuous at this point.

4. **At \( x = 2 \)**: The graph has an open circle, suggesting a discontinuity. However, the function approaches a value from both sides, but it does not exist at \( x = 2 \). This is a discontinuity where **neither the left nor the right** side is continuous.

5. **At \( x = 4 \)**: The graph drops down, showing a jump discontinuity. The function is **continuous from the left** but not from the right.

6. **At \( x = 6 \)**: The graph stops at \( x = 6 \) with an open circle, indicating a discontinuity. It is discontinuous from both sides, so **neither** side is continuous here.

### Summary of discontinuities:
- \( x = -4 \): Neither
- \( x = -2 \): Continuous from the left
- \( x = 2 \): Neither
- \( x = 4 \): Continuous from the left
- \( x = 6 \): Neither

Would you like more details on how to classify types of discontinuities or have any questions about the specific points on the graph?

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### Follow-up Questions:
1. What are the conditions for a function to be continuous at a point?
2. How is a "removable discontinuity" different from a "jump discontinuity"?
3. What does it mean for a function to be continuous from the right or left?
4. How can discontinuities affect the limit of a function at a given point?
5. What other types of discontinuities exist besides "jump" and "removable"?

### Tip:
For a function to be continuous at a point, the left-hand limit, right-hand limit, and the function's value at the point must all be equal.

Use the graph to determine the x-values at which f is discontinuous. For each x-value, determine whether f is continuous from the right, from the left, or neither. (Enter your answers from smallest to largest.)

Learn how to identify points of discontinuity in a function's graph and determine whether the function is continuous from the right, from the left, or neither. This problem covers key concepts in understanding limits and the behavior of functions at various points.

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