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From the graph of the function \( f(x) \), we need to find and classify all points of discontinuity.

### Steps to analyze the discontinuities:
1. **Identify points of discontinuity visually**: Discontinuities occur where the graph has breaks, jumps, or holes.
2. **Classify each discontinuity**: Discontinuities are usually classified as:
   - **Removable discontinuity**: The graph has a hole, and the limit exists, but the function value is not defined at that point or differs from the limit.
   - **Jump discontinuity**: The graph jumps at a point, i.e., the left and right-hand limits exist but are not equal.
   - **Infinite discontinuity**: The graph approaches infinity at the discontinuity, indicating a vertical asymptote.

### Observations:
- At \( x = -2 \): There is a **removable discontinuity**. There is a hole in the graph at \( x = -2 \), but the function value is defined just below the hole.
- At \( x = 1 \): There is a **jump discontinuity**. The graph has two different values when approaching from the left and the right, indicating a jump.
- At \( x = 2 \): There is an **infinite discontinuity**. The graph shoots off towards infinity, indicating a vertical asymptote.

### Summary of discontinuities:
1. **At \( x = -2 \)**: Removable discontinuity (hole in the graph).
2. **At \( x = 1 \)**: Jump discontinuity (function has a jump between two different values).
3. **At \( x = 2 \)**: Infinite discontinuity (vertical asymptote).

Would you like more details on any of these classifications or explanations?

### 5 Related Questions:
1. What is the definition of a removable discontinuity, and how is it different from a jump discontinuity?
2. Can you explain how limits behave around a jump discontinuity?
3. How can we formally determine the type of discontinuity using limits?
4. What happens to the function value at points of infinite discontinuity?
5. Can a function have both a removable discontinuity and an infinite discontinuity at the same point?

### Tip:
Always check the left-hand and right-hand limits of the function at points of discontinuity to properly classify them.

Let f(x) be given below by its graph. Find and classify all points of discontinuity.

Learn how to find and classify points of discontinuity in a function by analyzing its graph. This problem explains the types of discontinuities, including removable, jump, and infinite, using a detailed graph representation. Suitable for Grades 10-12.

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