Question

Describe the end behavior of the function f(x) = 4x⁵ - 16x² + 8.

Answer 1

The end behavior of the function f(x) = 4x⁵ - 16x² + 8 is that as x approaches positive infinity, the function increases without bound, and as x approaches negative infinity, the function decreases without bound.

Step-by-step explanation:

The end behavior of a function describes the behavior of the function as x approaches positive or negative infinity. To determine the end behavior of the function f(x) = 4x⁵ - 16x² + 8, we need to examine the leading term of the function, which is 4x⁵. Since the degree of this term is odd and the coefficient is positive, the end behavior of the function is as follows:

• As x approaches positive infinity, the function f(x) increases without bound.
• As x approaches negative infinity, the function f(x) decreases without bound.