he 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 left parenthesis 2 x minus 1 right parenthesis

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 2 x plus 1

g(x)=2x−1

Answer 1

To determine the function \( g(x) \) based on the rule "rx-axis," we need to reflect the function \( f(x) = -2x + 1 \) across the x-axis.

When we reflect a function across the x-axis, we negate the entire function. Therefore, we take the negative of \( f(x) \):

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

So, the correct selection for \( g(x) \) based on the reflection across the x-axis is:

g(x) = 2x - 1