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 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 minus 1

g(x)=2x+1

Answer 1

To find the function \( g(x) \) based on the transformation "reflecting over the x-axis" of the function \( f(x) = -2x + 1 \), we need to reflect the output of \( f(x) \).

Reflecting a function over the x-axis changes the sign of the function, so we would have:

\[ g(x) = -f(x) = -(-2x + 1) = 2x - 1 \]

Thus, the correct response is:

g(x) = 2x - 1