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

Answer 1

To determine when g(x) is greater than f(x), we can look at the values of g(x) and f(x) for each value of x given in the table.

Comparing g(x) and f(x) for each value of x:
- When x = -2, g(-2) = 3 > f(-2) = -1
- When x = -1, g(-1) = 3/4 > f(-1) = 3/4
- When x = 0, g(0) = 0 < f(0) = 1
- When x = 1, g(1) = 3/4 < f(1) = 1 1/4
- When x = 2, g(2) = 3 < f(2) = 3

Therefore, g(x) is greater than f(x) when x is less than -1 or when x is greater than -1. This means that:
- Option C: g(x) is greater than f(x) when x < -1
- Option A: g(x) is greater than f(x) when x < 2

So, the correct answer is:
A. g(x) is greater than f(x) when x < 2