Question

Compare the functions f(x) and g(x). When is g(x) greater than f(x)?
Table: x: -2, -1, 0, 1, 2
f(x): -1, 3/4, 1, 1 1/4, 3
g(x): 3, 3/4, 0, 3/4, 3

A. g(x) is greater than f(x) when x < 2
B. g(x) is greater than f(x) when x > -2
C. g(x) is greater than f(x) when x < -1
D. g(x) is greater than f(x) when x > -1

Answers

GPT 3.5
To compare the functions f(x) and g(x) at each given value of x, we see:

At x = -2, f(-2) = -1 and g(-2) = 3. Therefore, g(x) is greater than f(x) at x = -2.

At x = -1, f(-1) = 3/4 and g(-1) = 3/4. Both functions are equal at x = -1.

At x = 0, f(0) = 1 and g(0) = 0. Therefore, f(x) is greater than g(x) at x = 0.

At x = 1, f(1) = 1 1/4 and g(1) = 3/4. Therefore, f(x) is greater than g(x) at x = 1.

At x = 2, f(2) = 3 and g(2) = 3. Both functions are equal at x = 2.

Therefore, g(x) is greater than f(x) when x = -2 and x = -1. This means that g(x) is greater than f(x) when x > -2. So, the correct answer is:

B. g(x) is greater than f(x) when x > -2.