The function f(x)=−2x+1 is linear. Select the function g(x) based on the rule rx−axis.(1 point)

Question

Responses

g(x)=2x+1
g left parenthesis x right parenthesis equals 2 x plus 1

g(x)=2x−1
g left parenthesis x right parenthesis equals 2 x minus 1

g(x)=−(2x−1)
g left parenthesis x right parenthesis equals negative left parenthesis 2 x minus 1 right parenthesis

g(x)=−2x−1

Answer 1

To find the function \( g(x) \) based on the rule \( rx \) - axis transformation (reflecting across the x-axis) of the function \( f(x) = -2x + 1 \), we can follow these steps:

1. The reflection of a function \( f(x) \) across the x-axis is given by \( g(x) = -f(x) \).

2. Thus, we compute \( g(x) = -(-2x + 1) \).

3. Distributing the negative sign gives: \[ g(x) = 2x - 1 \]

So the correct function \( g(x) \) based on the rule \( rx \) - axis is:

g(x) = 2x - 1.