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

Answer 1

To find the function \( g(x) \) that corresponds to reflecting the function \( f(x) = -2x + 1 \) across the x-axis, we need to change the sign of the entire function. This means that we must multiply the function \( f(x) \) by \(-1\).

Starting with:

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

Reflecting this across the x-axis gives us:

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

So the function \( g(x) \) after reflection is:

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

From the provided responses, the correct choice is:

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

Or written in another format:

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