The function f (x) = -2x + 1 is linear. Select the function for g(x) based on the rule r_x-axis.

Question

A. g (x) = -(2x - 1)
B. g (x) = 2x + 1
C. g (x) = -2x - 1
D. g (x) = 2x -1

Answer 1

To find the function \( g(x) \) based on the rule \( r_{x\text{-axis}} \), we need to reflect the function \( f(x) = -2x + 1 \) across the x-axis. Reflecting a function across the x-axis means that we will negate the output of the function, resulting in \( g(x) = -f(x) \).

Starting with the original function: \[ f(x) = -2x + 1 \]

Now we negate it: \[ g(x) = -(-2x + 1) = 2x - 1 \]

Thus, the correct option for \( g(x) \) based on the rule \( r_{x\text{-axis}} \) is: D. g(x) = 2x - 1.