Question

The function f(x)=−2x+1 is linear. Select the function g(x) based on the rule rx−axis.

g(x)=2x+1

g(x)=2x−1

g(x)=−2x−1

g(x)=−(2x−1)

Answer 1

The rule "rx−axis" typically refers to reflecting the function across the x-axis. When you reflect a function \( f(x) \) across the x-axis, the new function \( g(x) \) is obtained by taking the negative of \( f(x) \).

Given the function:

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

To reflect it across the x-axis, we multiply by -1:

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

Thus, the correct function \( g(x) \) based on the reflection across the x-axis is:

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

So the answer is:

**g(x) = 2x−1**