Which compares the end behavior of the functions f and g?
f(x) = 9x + 2
g(x) = –4x – 7
A. For f, as x → ∞, f(x) → ∞. Likewise, for g, as x → ∞, g(x) → ∞.
B. For f, as x → ∞, f(x) → –∞. Likewise, for g, as x → ∞, g(x) → –∞.
C. For f, as x → ∞, f(x) → –∞. However, for g, as x → ∞, g(x) → ∞.
D. For f, as x → ∞, f(x) → ∞. However, for g, as x → ∞, g(x) → –∞.
The correct answer is D. For f, as x → ∞, f(x) → ∞. However, for g, as x → ∞, g(x) → –∞.
Explanation:
1. The function f(x) = 9x + 2 is a linear function with a positive slope (9). As x approaches infinity (x → ∞), the value of f(x) also approaches infinity (f(x) → ∞).
2. The function g(x) = –4x – 7 is a linear function with a negative slope (–4). As x approaches infinity (x → ∞), the value of g(x) decreases without bound, approaching negative infinity (g(x) → –∞).
So, as we analyze the end behavior, we see that f goes to infinity while g goes to negative infinity, which confirms option D. If you need further clarification or more information, please check the extended services page!