The function f(x)=−2x+1

Question

is linear. Select the function g(x)
based on the rule rx−axis
.(1 point)
Responses

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

g(x)=2x−1

Answer 1

To apply the rule "rx-axis" to the function \( f(x) = -2x + 1 \), we reflect the function over the x-axis. This transformation changes the sign of the output of the function, which means we replace \( f(x) \) with \( -f(x) \).

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

We reflect it over the x-axis: \[ g(x) = -f(x) = -(-2x + 1) = 2x - 1 \]

Therefore, the correct function \( g(x) \) based on the rule "rx-axis" is: \[ g(x) = 2x - 1 \]

So the answer is: \[ g(x) = 2x - 1 \]