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To determine the vertical and horizontal asymptotes from the graph of \( y = f(x) \):

### Vertical Asymptotes:
A vertical asymptote occurs where the function tends to infinity (positive or negative) as \( x \) approaches a certain value. In the graph:

- As \( x \) approaches \( -2 \) from both sides, the function tends to negative infinity. This indicates a **vertical asymptote at \( x = -2 \)**.
- As \( x \) approaches \( 3 \), the function grows without bound as well. This shows a **vertical asymptote at \( x = 3 \)**.

### Horizontal Asymptotes:
A horizontal asymptote occurs when the function approaches a specific \( y \)-value as \( x \) tends to infinity or negative infinity. In the graph:

- As \( x \) approaches negative infinity, the function appears to approach \( y = 1 \). This indicates a **horizontal asymptote at \( y = 1 \)**.
- As \( x \) approaches positive infinity, the function appears to approach \( y = -1 \). This indicates a **horizontal asymptote at \( y = -1 \)**.

### Conclusion:
- **Vertical asymptotes**: \( x = -2 \) and \( x = 3 \)
- **Horizontal asymptotes**: \( y = 1 \) and \( y = -1 \)

Would you like any more details on this explanation?

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### Related Questions:
1. What is the difference between a vertical and horizontal asymptote?
2. How do you determine asymptotes algebraically from a rational function?
3. Why can't a function cross a vertical asymptote but can cross a horizontal asymptote?
4. How do you find oblique asymptotes, and are there any in this graph?
5. How would a logarithmic function's asymptotes appear differently compared to this graph?

**Tip:** For rational functions, vertical asymptotes occur at values of \( x \) that make the denominator zero (without canceling with the numerator). Horizontal asymptotes depend on the degrees of the numerator and denominator.

Determine the vertical and horizontal asymptotes of the function based on the graph of y = f(x).

This problem involves identifying the vertical and horizontal asymptotes of a function using a graphical representation. Learn how to determine asymptotes by analyzing the behavior of the function as it approaches infinity or certain x-values.

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