Final answer:
The end behavior of the polynomial function f(x) = x^3 - 3x - 2 is that as x approaches infinity, f(x) approaches infinity, and as x approaches negative infinity, f(x) approaches negative infinity. Option A is the correct answer.
Step-by-step explanation:
To identify the end behavior of the polynomial function f(x) = x3 - 3x - 2, we should look at the highest power of x. As the degree of the polynomial is odd (3) and the leading coefficient is positive (1), we can determine the end behavior.
As x approaches infinity, the x3 term dominates the behavior of the function, leading to f(x) increasing without bound. Hence, as x → [infinity], f(x) → [infinity].
Conversely, as x approaches negative infinity, the x3 term still dictates the behavior, but since cubing a negative number yields a negative result, f(x) decreases without bound. Therefore, as x → -[infinity], f(x) → -[infinity].
The correct option answer for the end behavior of the function f(x) = x3 - 3x - 2 is: a) As x → [infinity], f(x) → [infinity] and as x → -[infinity], f(x) → -[infinity].