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The problem is about analyzing the behavior of a function \( f(x) \) as \( x \) approaches various values based on the given graph, focusing on limits. Here's a breakdown of each part based on the image:

- **g.** You are asked to select the correct choice for \( \lim_{x \to -2} f(x) \).
  - Based on the graph, as \( x \to -2 \), \( f(x) \) approaches positive infinity (\( +\infty \)), so the correct answer is **A**: \( \lim_{x \to -2} f(x) = \infty \).

- **h.** You are asked to evaluate \( \lim_{x \to 1^+} f(x) \), meaning the limit as \( x \) approaches 1 from the right.
  - From the graph, as \( x \to 1^+ \), the function approaches \( +\infty \), so the correct answer is \( \infty \).

- **i.** You are asked to evaluate \( \lim_{x \to 1^-} f(x) \), meaning the limit as \( x \) approaches 1 from the left.
  - As \( x \to 1^- \), the graph shows that \( f(x) \) approaches \( -\infty \), so the correct answer is \( -\infty \).

- **j.** You are asked to evaluate \( \lim_{x \to 1} f(x) \), but you are selecting between two choices.
  - Since the left-hand limit \( \lim_{x \to 1^-} f(x) = -\infty \) and the right-hand limit \( \lim_{x \to 1^+} f(x) = +\infty \), the two limits do not match. Therefore, the correct answer is **B**: The limit does not exist and is neither \( -\infty \) nor \( +\infty \).

- **k.** You are asked to evaluate \( \lim_{x \to \infty} f(x) \).
  - As \( x \) approaches infinity, \( f(x) \) approaches 1, so the correct answer is \( 1 \).

If you need more clarification or details on any part, feel free to ask!

### Additional Related Questions:
1. What is the difference between left-hand and right-hand limits?
2. How does vertical asymptotic behavior affect the limit of a function?
3. Why does a limit not exist when the left and right limits differ?
4. Can a function have finite limits at infinity, and what does it signify graphically?
5. How do we determine horizontal asymptotes from the graph of a function?

### Tip:
Always check both the left-hand and right-hand limits when dealing with points of discontinuity, as they provide insight into whether the limit exists.

For the function f whose graph is given, determine the limits in parts a through l below. Write ∞ or -∞ where appropriate.

This problem explores the behavior of a function f(x) as x approaches various values, including ∞ and -∞. Learn how to determine one-sided limits, identify asymptotes, and understand when limits do not exist. A detailed step-by-step solution suitable for Grades 10-12.

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