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The function given is \( f(x) = -x^6 \).

### To describe the end behavior of \( f(x) \), let's analyze both as \( x \to \infty \) and \( x \to -\infty \):

1. **As \( x \to \infty \)**:
   - When \( x \to \infty \), the term \( x^6 \) becomes very large because it is a positive even power of \( x \). However, since there is a negative sign in front of \( x^6 \), \( f(x) = -x^6 \) becomes very negative. 
   - Therefore, as \( x \to \infty \), \( f(x) \to -\infty \).

2. **As \( x \to -\infty \)**:
   - When \( x \to -\infty \), \( (-x)^6 \) is still positive because any even power of a negative number results in a positive number. Again, due to the negative sign in front of \( x^6 \), \( f(x) = -x^6 \) will still approach very large negative values.
   - Therefore, as \( x \to -\infty \), \( f(x) \to -\infty \).

### Conclusion:
- As \( x \to \infty \), \( f(x) \to -\infty \).
- As \( x \to -\infty \), \( f(x) \to -\infty \).

Would you like more details on any specific part of this explanation?

Here are 5 related questions:
1. What is the end behavior of \( f(x) = x^6 \)?
2. How does the degree of a polynomial affect its end behavior?
3. What happens if the leading term of a polynomial has a negative coefficient?
4. How do odd-degree polynomials behave as \( x \to \infty \) and \( x \to -\infty \)?
5. Can you explain the difference in end behavior between even and odd power functions?

**Tip**: The leading term of a polynomial (the term with the highest exponent) determines the end behavior of the function.

Describe the end behavior (long run behavior) of f(x) = -x^6.

Analyze the end behavior of the polynomial function f(x) = -x^6. Learn how even exponents and negative leading coefficients influence the long run behavior of polynomials. Suitable for students in Grades 10-12.

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