Question

The function f(x)=−2x+1 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 2 x plus 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 obtain the function \( g(x) \) based on the reflection of \( f(x) = -2x + 1 \) across the x-axis, we need to negate the output of \( f(x) \).

Given:

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

The reflection across the x-axis would be:

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

Simplifying that, we have:

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

So the correct answer is:

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

Thus, the choice is:

**\( g(x) = 2x - 1 \)**