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

For the given function f(x) = (x + 6)² + 2, as x approaches positive infinity, the value of f(x) will also approach positive infinity. Therefore, the correct option for the end behavior as x approaches positive infinity is (a) f(x) approaches positive infinity.

Step-by-step explanation:

The end behavior of a function describes what happens to the values of f(x) as x approaches infinity or negative infinity. For the function f(x) = (x + 6)² + 2, as x approaches positive infinity, the x term becomes much larger than the constant terms, making the x-dependent term dominate the equation.

Since squaring a very large positive number results in an even larger positive number, and adding 2 to this will still result in a positive number that gets larger as x gets larger, f(x) also approaches infinity. Therefore, the correct option for the end behavior as x approaches positive infinity is (a) f(x) approaches positive infinity.