Question

As x approaches infinity, for which function does f(x) approach negative infinity? Select all that apply.

1) f(x) = 1/x
2) f(x) = x²
3) f(x) = -x
4) f(x) = e⁽⁻ˣ⁾

Answer 1

The function f(x) = -x approaches negative infinity as x approaches infinity.

Step-by-step explanation:

To determine which function approaches negative infinity as x approaches infinity, we can analyze the behavior of each function.

1) f(x) = 1/x: As x approaches infinity, the value of 1/x approaches 0, not negative infinity.

2) f(x) = x²: As x approaches infinity, the value of x² also approaches infinity, not negative infinity.

3) f(x) = -x: As x approaches infinity, the value of -x approaches negative infinity, so this function does approach negative infinity.

4) f(x) = e⁽⁻ˣ⁾: As x approaches infinity, the value of e⁽⁻ˣ⁾ approaches 0, not negative infinity.

Therefore, the functions that approach negative infinity as x approaches infinity are f(x) = -x.