Question

End Behavior Falls to Left and Falls to Right

Determine the end behavior of the polynomial function f(x) = 2x³ - 5x² + 3x + 1.
a) Falls to the left and falls to the right.
b) Rises to the left and falls to the right.
c) Falls to the left and rises to the right.
d) Rises to the left and rises to the right.

Answer 1

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.