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This question asks for the end behavior of the given polynomials. Let's solve each part:

### (a) \( y = x^3 - 3x^2 + 2x - 11 \)
- The leading term (which determines the end behavior) is \( x^3 \).
- Since the degree is odd and the leading coefficient is positive:
  - As \( x \to \infty \), \( y \to \infty \).
  - As \( x \to -\infty \), \( y \to -\infty \).

### (b) \( y = -2x^4 + 16x + 500 \)
- The leading term is \( -2x^4 \).
- Since the degree is even and the leading coefficient is negative:
  - As \( x \to \infty \), \( y \to -\infty \).
  - As \( x \to -\infty \), \( y \to -\infty \).

#### Summary:
- (a) End behavior:
  - \( y \to \infty \) as \( x \to \infty \).
  - \( y \to -\infty \) as \( x \to -\infty \).
- (b) End behavior:
  - \( y \to -\infty \) as \( x \to \infty \).
  - \( y \to -\infty \) as \( x \to -\infty \).

Would you like further clarification or more details on this?

Here are some related questions for further practice:
1. What happens to the end behavior if the leading coefficient changes its sign?
2. How does the degree of the polynomial affect its graph's overall shape?
3. Can you describe the end behavior of a polynomial of even degree with a positive leading coefficient?
4. What would the end behavior be for \( y = 5x^5 - 2x^3 + x \)?
5. How does the degree of a polynomial relate to the number of turning points?

**Tip:** The degree and the sign of the leading coefficient are the key factors in determining the end behavior of a polynomial.

Describe the end behavior of each polynomial.

Learn how to describe the end behavior of polynomial functions like y = x^3 - 3x^2 + 2x - 11 and y = -2x^4 + 16x + 500. This explanation covers concepts like the leading term and how it determines the behavior as x approaches infinity or negative infinity. Suitable for high school students.

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