Final answer:
For large values of |x|, the function f(x) = -x²(x + 3)³(x² - 1) resembles the power function -x⁷.
Step-by-step explanation:
The student asked to find the power function that approximates the behavior of the function f(x) = -x²(x + 3)³(x² - 1) for large values of |x|. In order to determine the power function, we can look at the highest degree term in the polynomial, since the other terms become relatively insignificant as |x| gets very large. The leading term of f(x) is the product of the highest power terms, which is -x² × x³ × x² = -x⁷. Hence, for large values of |x|, the function f(x) resembles the power function -x⁷.