Question

the function g(x) is shown in the table. suppose f(x) = 4x - 2. when comparing the functions, which describes the x - value when g(x) becomes greater than f(x)?
a the x - value is between 1 and 2
b the x - value is between 2 and 3
c the x - value is between 3 and 4
d the x - value is between 4 and 5

Explanation:

Step1: Calculate f(x) at x=3,4,5

For \( f(x) = 4x - 2 \):

• At \( x = 3 \): \( f(3) = 4(3) - 2 = 10 \)
• At \( x = 4 \): \( f(4) = 4(4) - 2 = 14 \)
• At \( x = 5 \): \( f(5) = 4(5) - 2 = 18 \)

Step2: Compare g(x) and f(x)

From the table:

• \( g(3) = 9 \), \( f(3) = 10 \) (so \( g(3) < f(3) \))
• \( g(4) = 16 \), \( f(4) = 14 \) (so \( g(4) > f(4) \))

Thus, \( g(x) \) becomes greater than \( f(x) \) between \( x = 3 \) and \( x = 4 \).

Answer:

C. The x - value is between 3 and 4