Final answer:
The end behavior of the polynomial function f(x) is that it rises to the left and falls to the right because the highest power term is 2x³ with a positive coefficient.
Step-by-step explanation:
To determine the end behavior of the polynomial function f(x) = 2x³ - 5x² + 3x + 1, we need to look at the highest power term, since it dominates the end behavior of the polynomial as x becomes very large or very small. In this case, the highest power term is 2x³.
The coefficient of the highest power term is positive, which means that as x approaches infinity (x → ∞), the function will rise to the right. As x approaches negative infinity (x → -∞), the function will fall to the left because of the odd exponent on the x term. Therefore, the correct choice is:
b) Rises to the left and falls to the right.