https://file.aiquickdraw.com/mathbot/file/17256226965354uyqlj3o.jpg

The question asks about the end behavior of the graph shown, with multiple choices. Let's analyze the graph and find the correct answer.

### Observing the Graph:
- On the left side, as \( x \to -\infty \), the graph appears to decrease, with \( y \to -\infty \).
- On the right side, as \( x \to \infty \), the graph also decreases with \( y \to -\infty \).

### Matching this with the provided answer choices:
The correct option is:
- **As \( x \to -\infty \), \( y \to \infty \) and as \( x \to \infty \), \( y \to -\infty \)**

This matches the downward trend of the graph on both ends.

Would you like further details or have any questions about end behavior?

Here are five related questions to consider:
1. How is the end behavior of a polynomial function determined?
2. What does the degree of a polynomial tell you about its end behavior?
3. How can you analyze the end behavior of a rational function?
4. What is the impact of leading coefficient on the end behavior?
5. How does symmetry (odd vs even functions) influence end behavior?

**Tip:** Always check the highest degree term in a function to predict its end behavior.

This problem explores the end behavior of a polynomial graph, requiring students to analyze how the graph behaves as x approaches positive and negative infinity. Suitable for high school students, this problem develops graph analysis skills.

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