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Looking at the graph, we can observe the behavior of the function as \( x \) approaches positive and negative infinity.

- The **upper horizontal asymptote**: As \( x \) goes to infinity (to the right side), the function approaches \( y = 1 \). This can be observed as the function flattens out near \( y = 1 \) for large positive values of \( x \).

- The **lower horizontal asymptote**: As \( x \) goes to negative infinity (to the left side), the function approaches \( y = -2 \). This can be seen as the function flattens out near \( y = -2 \) for large negative values of \( x \).

Therefore, the equations of the horizontal asymptotes are:

- Upper asymptote: \( y = 1 \)
- Lower asymptote: \( y = -2 \)

Would you like more details on how to find horizontal asymptotes or clarification on any part?

Here are some related questions for practice:
1. How do you calculate horizontal asymptotes for rational functions?
2. What is the difference between horizontal and vertical asymptotes?
3. Can a function have more than one horizontal asymptote?
4. How do horizontal asymptotes affect the behavior of a function at infinity?
5. Can horizontal asymptotes cross the graph of a function?

**Tip:** Always check the behavior of a function as \( x \to \infty \) and \( x \to -\infty \) to determine horizontal asymptotes.

What are the horizontal asymptotes of the function in the figure? Define the equation of the upper and lower asymptote of the function.

Learn how to determine the horizontal asymptotes for a given function by analyzing its graph. This problem focuses on identifying the upper and lower horizontal asymptotes, suitable for students in Grades 10-12.

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