https://file.aiquickdraw.com/mathbot/file/1726070060315nnm6rlag.jpg

Let's analyze the graph to determine the truth of each statement:

1. **Jump Discontinuity at \( x = 1 \):**
   At \( x = 1 \), the graph has an open circle (the function is not defined at this point) and a filled dot at a different height, indicating that the left-hand limit does not equal the right-hand limit. This is a classic jump discontinuity.

2. **Removable Discontinuity at \( x = 0 \):**
   At \( x = 0 \), the graph shows a hole (open circle) but the function value seems to approach the same point from both sides. This suggests that the limit exists but the function is not defined at this point, making it a removable discontinuity.

3. **Infinite Discontinuity at \( x = -2 \):**
   At \( x = -2 \), the graph has a vertical asymptote, indicating that the function goes to infinity on both sides of this point. This is an infinite discontinuity.

### Conclusion:
- All three statements are true.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. What is the definition of a jump discontinuity?
2. How is a removable discontinuity different from other types of discontinuities?
3. What causes an infinite discontinuity in a function?
4. Can a function have more than one type of discontinuity at a single point?
5. How can you determine the limit of a function graphically?

**Tip:** Always check both the left-hand and right-hand limits to determine the type of discontinuity at a point.

The graph of a function f(x) is shown below. How many of the following statements are true?

- f(x) has a jump discontinuity at x = 1
- f(x) has a removable discontinuity at x = 0
- f(x) has an infinite discontinuity at x = -2

Explore how to identify different types of discontinuities in a function graph, including jump, removable, and infinite discontinuities. Learn how these concepts apply to analyzing a function visually, suitable for high school students in Grades 10-12.

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