https://file.aiquickdraw.com/mathbot/file/17278435981182epudm6o.jpg

The image you provided depicts a function graph that appears to be a rational or piecewise function, and it includes potential discontinuities. Discontinuities typically occur where:

- The function is undefined (division by zero or other undefined behavior).
- There is a jump (sudden change in function value).
- There is an infinite discontinuity (asymptote).

By examining the graph, we can infer discontinuous points:

1. At **x = -2**, the graph shows an open circle, which suggests a **removable discontinuity**. This means the function is not defined at this point but may be defined nearby.
2. At **x = 2**, another open circle exists, indicating another **removable discontinuity**.
3. There also appears to be a vertical asymptote at **x = 0**, which suggests an **infinite discontinuity**. The function approaches infinity as \(x\) approaches 0 from both directions.

### Discontinuous Points:
- **x = -2** (removable discontinuity)
- **x = 2** (removable discontinuity)
- **x = 0** (infinite discontinuity)

Would you like further details on different types of discontinuities or more information about this graph?

Here are five questions that can expand your understanding:

1. What is the difference between a removable and a non-removable discontinuity?
2. How do we algebraically identify discontinuities in rational functions?
3. Can you explain why a vertical asymptote causes an infinite discontinuity?
4. How can piecewise functions result in jump discontinuities?
5. What are other common types of discontinuities in graphs of functions?

**Tip:** To determine whether a discontinuity is removable or non-removable, check if you can redefine the function at the discontinuous point to make it continuous.

Find the points where the function is discontinuous based on the provided graph.

Learn how to identify the points of discontinuity in a rational function graph. This problem includes understanding removable and infinite discontinuities, and the impact of vertical asymptotes. Suitable for high school students in Grades 11-12.

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