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The problem provides several key limits and function values for \( f(x) \). Let's break it down:

1. **Behavior around \( x = 2 \)**:
   - \( \lim_{x \to 2^-} f(x) = -\infty \) indicates a vertical asymptote at \( x = 2 \), where the function goes to \( -\infty \) as \( x \) approaches 2 from the left.
   - \( \lim_{x \to 2^+} f(x) = \infty \) indicates the function goes to \( \infty \) as \( x \) approaches 2 from the right. So, there's a jump discontinuity at \( x = 2 \).

2. **Behavior as \( x \to -\infty \)**:
   - \( \lim_{x \to -\infty} f(x) = 2 \) implies there is a horizontal asymptote at \( y = 2 \) as \( x \to -\infty \).

3. **Behavior as \( x \to \infty \)**:
   - \( \lim_{x \to \infty} f(x) = 2 \) suggests another horizontal asymptote at \( y = 2 \) as \( x \to \infty \).

4. **Behavior around \( x = 3 \)**:
   - \( \lim_{x \to 3^-} f(x) = 5 \) and \( \lim_{x \to 3^+} f(x) = 5 \), which means the function approaches 5 from both sides of \( x = 3 \), but \( f(3) \) is undefined. This implies a hole at \( x = 3 \).

5. **Function values**:
   - \( f(1) = 0 \) gives a point at \( (1, 0) \), which is an x-intercept.
   - \( f(0) = 1 \) gives another point at \( (0, 1) \).

### Sketching the Graph
Based on this information, the graph would exhibit the following features:
- A vertical asymptote at \( x = 2 \).
- A horizontal asymptote at \( y = 2 \) for both \( x \to -\infty \) and \( x \to \infty \).
- A hole at \( x = 3 \), \( y = 5 \).
- Intercepts at \( (1, 0) \) and \( (0, 1) \).

Would you like more details on the sketching process, or clarification on specific parts?

Here are five related questions:
1. How do vertical asymptotes influence the graph of a function?
2. What is the significance of horizontal asymptotes in behavior as \( x \to \infty \) and \( x \to -\infty \)?
3. How do you interpret jump discontinuities like the one at \( x = 2 \)?
4. What is the difference between a removable discontinuity (like the hole at \( x = 3 \)) and a non-removable one?
5. How does knowing \( f(1) = 0 \) and \( f(0) = 1 \) help in plotting points?

**Tip:** When sketching graphs of functions, always start with identifying the behavior at critical points like asymptotes, intercepts, and discontinuities.

Consider the following information about f(x): lim x→2⁻ f(x) = -∞, lim x→2⁺ f(x) = ∞, lim x→-∞ f(x) = 2, lim x→∞ f(x) = 2, lim x→3⁻ f(x) = 5, lim x→3⁺ f(x) = 5, f(3) = undefined, f(1) = 0, f(0) = 1. Sketch the graph indicating all asymptotes, intercepts, and discontinuities.

Learn how to graph a function based on limits and discontinuities, focusing on vertical and horizontal asymptotes, intercepts, and undefined points. This example covers essential calculus concepts such as jump discontinuities and holes in the graph, suitable for Grades 11-12.

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