Question

Given the function below, which of the following describes the end behavior as x approaches positive infinity?

f(x) = (x - 6)²+ 2

a. f(x) approaches positive infinity
b. f(x) approaches negative infinity
c. f(x) approaches 6
d. f(x) approaches -6

Answer 1

The end behavior of the given function as x approaches positive infinity is that f(x) approaches positive infinity. (option a)

Step-by-step explanation:

The given function is f(x) = (x - 6)² + 2a. To determine the end behavior as x approaches positive infinity, we need to look at the leading term of the function. The leading term is (x - 6)², which is a quadratic term. As x approaches positive infinity, the quadratic term will keep getting larger and larger, resulting in f(x) approaching positive infinity.

Therefore, the correct option is a. f(x) approaches positive infinity.