The correct statement is: d. approaches -∞ as x approaches -∞, f(x) approaches ∞ as x approaches ∞, and f(x) approaches ∞ as x approaches -∞.
The end behavior of the function 9 - 3x+ 4x^4 2x^3 can be determined by looking at the term with the highest exponent.
In this case, the term with the highest exponent is x⁴, which is of degree 4. Since the highest degree term is positive and even, the function approaches infinity as x approaches both positive and negative infinity. Therefore, the correct statement is:
d. approaches -∞ as x approaches -∞, f(x) approaches ∞ as x approaches ∞, and f(x) approaches ∞ as x approaches -∞