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

Question

G(x)=2x-1
G(x)=2x+1
G(x)=-2x-1
G(x)=-(2x-1)

Answer 1

To apply the reflection rule across the x-axis to the function \( f(x) = -2x + 1 \), we need to change the sign of the entire function.

Given \( f(x) = -2x + 1 \), reflecting it across the x-axis gives us:

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

Thus, the function \( g(x) \) after reflecting \( f(x) \) across the x-axis is:

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

So the correct choice is:

G(x) = 2x - 1.