Final answer:
The end behavior of the function f(x) = 2x⁵ + 3x³ - x + 2 is that as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.
Step-by-step explanation:
The end behavior of a function describes what happens to the function as the input (x-values) approaches positive or negative infinity. To determine the end behavior of the function f(x) = 2x⁵ + 3x³ - x + 2, we need to examine the power (degree) of the highest term.
In this case, the highest power term is 2x⁵. Since the power of x is odd (positive and odd), the end behavior of the function f(x) is similar to the end behavior of a cubic function.
As x approaches positive infinity, the function f(x) also approaches positive infinity. As x approaches negative infinity, the function f(x) approaches negative infinity.