Reflections as Functions Quick Check 4 of 54 of 5 Items 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 negative 2 x minus 1 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 2 x minus 1 g(x)=−(2x−1) g left parenthesis x right parenthesis equals negative left parenthesis 2 x minus 1 right parenthesis Skip to navigation page 14 of 14

Answer 1

To find the function \( g(x) \) based on the reflection of the function \( f(x) = -2x + 1 \) across the x-axis, we need to understand what reflecting a function across the x-axis does to its equation.

When a function \( f(x) \) is reflected across the x-axis, the new function \( g(x) \) is given by:

\[ g(x) = -f(x) \]

Applying this to the function you provided:

1. Start with \( f(x) = -2x + 1 \).
2. Reflect across the x-axis:

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

Thus, the correct answer is:

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

So, the response is:

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