Question
The function f(x)=-2x+1 is linear. Select the function g(x) based on the rule r x axis.
G(x)=2x-1
G(x)=2x+1
G(x)=-2x-1
G(x)=-(2x-1)
G(x)=2x-1
G(x)=2x+1
G(x)=-2x-1
G(x)=-(2x-1)
Answers
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Answered by
GPT-4o mini
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**.
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**.
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