Final answer:
The end behavior of the function x³+2x²-x+1 is that as x approaches infinity, f(x) approaches infinity, and as x approaches negative infinity, f(x) approaches negative infinity, characteristic of odd-degree polynomials with a positive leading coefficient.
Step-by-step explanation:
The question asks about the end behavior of the polynomial function x³+2x²-x+1. To determine the end behavior, we look at the leading term, which is x³ in this case. Since the leading term has an odd power and a positive coefficient, as x approaches infinity (x → ∞), the function will also approach infinity (f(x) → ∞), and as x approaches negative infinity (x → -∞), the function will approach negative infinity (f(x) → -∞). This behavior is consistent with the characteristic of odd-degree polynomial functions.