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The problem asks to determine several limits of the function \( f(x) \), based on the graph provided. I'll analyze the function graph and help determine each limit.

### Graph Details:
- The graph shows a function \( f(x) \) with distinct behaviors at various points of interest, such as:
  - \( x = -\infty \)
  - \( x = -2 \)
  - \( x = 0 \)
  - \( x = 1 \)
  - \( x = +\infty \)

### Limits to Calculate:
1. \( \lim_{x \to -\infty} f(x) \)
2. \( \lim_{x \to -2^-} f(x) \)
3. \( \lim_{x \to -2^+} f(x) \)
4. \( \lim_{x \to 0^-} f(x) \)
5. \( \lim_{x \to 0^+} f(x) \)
6. \( \lim_{x \to 1^-} f(x) \)
7. \( \lim_{x \to 1^+} f(x) \)
8. \( \lim_{x \to +\infty} f(x) \)

### Solution:

1. **\( \lim_{x \to -\infty} f(x) \):**
   - As \( x \to -\infty \), the graph shows that \( f(x) \to -\infty \).
   
2. **\( \lim_{x \to -2^-} f(x) \):**
   - Approaching \( x = -2 \) from the left, the graph shows a sharp decline. Hence, \( f(x) \to -\infty \).
   
3. **\( \lim_{x \to -2^+} f(x) \):**
   - Approaching \( x = -2 \) from the right, the function jumps to \( f(x) \to +\infty \).

4. **\( \lim_{x \to 0^-} f(x) \):**
   - As \( x \to 0 \) from the left, the function approaches a value near 1, i.e., \( f(x) \to 1 \).
   
5. **\( \lim_{x \to 0^+} f(x) \):**
   - As \( x \to 0 \) from the right, the function also approaches 1. Thus, \( f(x) \to 1 \).

6. **\( \lim_{x \to 1^-} f(x) \):**
   - As \( x \to 1 \) from the left, the graph shows the function approaching 0. Hence, \( f(x) \to 0 \).
   
7. **\( \lim_{x \to 1^+} f(x) \):**
   - Approaching \( x = 1 \) from the right, the function remains close to 0, so \( f(x) \to 0 \).

8. **\( \lim_{x \to +\infty} f(x) \):**
   - As \( x \to +\infty \), the graph shows that \( f(x) \to 0 \).

### Final Answers:
- (a) \( \lim_{x \to -\infty} f(x) = -\infty \)
- (b) \( \lim_{x \to -2^-} f(x) = -\infty \)
- (c) \( \lim_{x \to -2^+} f(x) = +\infty \)
- (d) \( \lim_{x \to 0^-} f(x) = 1 \)
- (e) \( \lim_{x \to 0^+} f(x) = 1 \)
- (f) \( \lim_{x \to 1^-} f(x) = 0 \)
- (g) \( \lim_{x \to 1^+} f(x) = 0 \)
- (h) \( \lim_{x \to +\infty} f(x) = 0 \)

Let me know if you'd like more details or have any questions!

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Here are some related questions:
1. What happens if a limit does not exist at a certain point?
2. Can a function have different limits from the left and the right at the same point?
3. What is the meaning of vertical asymptotes in terms of limits?
4. How do you calculate limits for piecewise functions?
5. What does it mean when a limit approaches infinity?

**Tip**: When limits from the left and right differ at a point, the two-sided limit does not exist. This is a common cause of discontinuities!

Determine the limits of the function based on the provided graph of f(x).

Learn how to determine various limits of a function by analyzing its graph. This problem explores fundamental concepts such as one-sided limits, behavior at infinity, and points of discontinuity, suitable for students in Grades 10-12.

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