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We are asked to determine the end behavior of the polynomial function:

\[
q(x) = -2x^8 + 5x^6 - 3x^5 + 50
\]

### Analyzing the polynomial:
- The highest-degree term, \(-2x^8\), dominates the behavior of the function as \( x \to \infty \) or \( x \to -\infty \).
- Since the degree of the polynomial is even (degree 8) and the leading coefficient is negative (\(-2\)), this tells us about the end behavior:
  - As \( x \to \infty \), \( q(x) \to -\infty \) because the leading term \( -2x^8 \) tends to negative infinity.
  - As \( x \to -\infty \), \( q(x) \to -\infty \) for the same reason: \( (-x)^8 \) is still positive, but multiplied by the negative coefficient, it tends to negative infinity.

### Conclusion:
- The correct answer is **D**: 
  \[
  \text{As } x \to \infty, q(x) \to -\infty, \text{ and as } x \to -\infty, q(x) \to -\infty.
  \]

Would you like further clarification or more details? 

Here are some related questions for deeper understanding:
1. How do you determine the end behavior of a polynomial based on its leading term?
2. What happens to a polynomial with an odd-degree leading term as \(x \to \infty\) and \(x \to -\infty\)?
3. How does the sign of the leading coefficient affect the end behavior of the function?
4. What would the end behavior be if the leading coefficient were positive instead of negative in this function?
5. Can the lower-degree terms (like \(5x^6\)) affect the end behavior of the polynomial?

**Tip:** Focus on the highest-degree term of a polynomial when determining its end behavior, as it dominates the behavior for very large or very small \(x\)-values.

Consider the polynomial function q(x) = -2x^8 + 5x^6 - 3x^5 + 50. What is the end behavior of the graph of q?

Learn how to determine the end behavior of the polynomial function q(x) = -2x^8 + 5x^6 - 3x^5 + 50. This problem covers key concepts related to polynomial functions, including the role of the leading term in determining end behavior. Suitable for high school students.

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