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The question is asking about the behavior of the polynomial function \( f(x) = -2x^3 - 2x^2 + 7x - 25 \) as \( x \to -\infty \), specifically if \( f(x) \to \infty \).

### Let's analyze the end behavior of the polynomial:

1. The highest-degree term of the polynomial is \( -2x^3 \). 
2. When \( x \to -\infty \), the cubic term \( x^3 \) will be negative because cubing a negative number results in a negative value.
3. The coefficient of \( x^3 \) is \( -2 \), which makes the highest-degree term \( -2x^3 \) positive when \( x \to -\infty \) (because multiplying two negatives gives a positive value).
4. Since the leading term dominates the behavior of the polynomial as \( x \to -\infty \), the function will tend to \( +\infty \) as \( x \to -\infty \).

Thus, the statement is **True**.

Would you like more details on the reasoning behind this? Here are five related questions you can consider:

1. What determines the end behavior of a polynomial function?
2. How does the degree and leading coefficient of a polynomial influence its behavior at \( \pm \infty \)?
3. What happens to the polynomial \( f(x) \) as \( x \to +\infty \)?
4. How do lower-degree terms affect the end behavior of a polynomial?
5. Why does the cubic term dominate over the other terms in this polynomial?

**Tip:** The end behavior of a polynomial is entirely determined by its highest-degree term!

For the polynomial f(x) = -2x^3 - 2x^2 + 7x - 25, as x → -∞, f(x) → ∞. Is this statement True or False?

Learn how to determine the end behavior of the polynomial f(x) = -2x^3 - 2x^2 + 7x - 25. Explore how the leading term affects the behavior as x tends to -∞. Suitable for precalculus students in Grades 10-12.

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