https://file.aiquickdraw.com/mathbot/file/1726595038783spl2iz22.jpg

Let's analyze the graph and answer the questions.

### Part a: End Behavior of the Graph
To determine the end behavior, we look at how the graph behaves as \( x \) approaches positive infinity (\( +\infty \)) and negative infinity (\( -\infty \)).

- As \( x \to -\infty \), the graph rises upwards, meaning \( y \to \infty \).
- As \( x \to \infty \), the graph falls downwards, meaning \( y \to -\infty \).

Thus, the correct choice for the end behavior is:
- **"As \( x \to -\infty \), \( y \to \infty \), and as \( x \to \infty \), \( y \to -\infty \)."**

This corresponds to the **third option**.

### Part b: Degree of the Polynomial
The end behavior indicates whether the polynomial is of odd or even degree:

- For **odd-degree polynomials**, the ends of the graph move in opposite directions (one side goes up while the other goes down).
- For **even-degree polynomials**, both ends of the graph move in the same direction (both up or both down).

Since the graph moves up on the left and down on the right, this represents an **odd-degree** polynomial. Therefore, the answer is **odd**.

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Would you like more details on the concept of end behavior or degree of polynomials?

Here are 5 follow-up questions for further exploration:
1. What specific characteristics differentiate odd-degree from even-degree polynomials?
2. How can you determine the leading coefficient of a polynomial from its graph?
3. How do turning points in the graph relate to the degree of the polynomial?
4. What does the symmetry (or lack of symmetry) of a polynomial's graph suggest about its degree?
5. How does the end behavior change if the leading coefficient of an odd-degree polynomial is negative?

**Tip:** Always remember, for odd-degree polynomials, the end behaviors on the left and right will be opposite, while for even-degree polynomials, they will be the same.

Analyze the end behavior of the graph and determine if it represents an odd-degree or even-degree polynomial.

Learn how to analyze the end behavior of a graph to determine if it represents an odd-degree or even-degree polynomial. This problem involves key concepts in algebra and calculus related to polynomial graph analysis, suitable for students in Grades 9-12.

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