https://file.aiquickdraw.com/mathbot/file/1726598526780l9t734j1.jpg

From the graph you provided, it appears to be a rational function with vertical and horizontal asymptotes.

### Vertical Asymptotes:
The graph shows two vertical lines approaching \( x = -1 \) and \( x = 3 \), which indicates **vertical asymptotes** at these points.

### Horizontal Asymptote:
The graph approaches \( y = 0 \) as \( x \to \infty \) and \( x \to -\infty \), indicating a **horizontal asymptote** at \( y = 0 \).

### Conclusion:
Based on the graph, the correct asymptotes are:
- \( x = -1 \)
- \( x = 3 \)
- \( y = 0 \)

### Answer Choices:
- \( x = -1 \) ✔️
- \( y = -2 \) ✖️ (not an asymptote)
- \( x = 3 \) ✔️
- \( x = 0 \) ✖️ (not an asymptote)
- \( y = 0 \) ✔️
- \( y = -3 \) ✖️ (not an asymptote)

Would you like further explanation on asymptotes, or do you have any questions?

Here are 5 related questions to deepen your understanding:
1. How do vertical asymptotes differ from horizontal asymptotes?
2. What is the equation of a rational function with the same asymptotes as shown in the graph?
3. How can you identify asymptotes algebraically from a rational function?
4. Why do rational functions often have vertical asymptotes?
5. How would the graph change if there was a slant asymptote instead of a horizontal asymptote?

**Tip:** Asymptotes describe the behavior of a function as it approaches infinity or specific points where the function is undefined.

Find the asymptotes of the function. Select all that apply.

Learn how to identify vertical and horizontal asymptotes from the graph of a rational function. This problem involves analyzing the graph to find the points where the function approaches infinity or zero. Suitable for students in Grades 10-12.

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