To reflect the function \( f(x) = -2x + 1 \) across the x-axis, we need to change the sign of the output (the function value). This reflection is achieved by taking the negative of the original function.
Thus, the function \( g(x) \) that reflects \( f(x) \) across the x-axis can be defined as:
\[ g(x) = -f(x) \]
Substituting \( f(x) \) into this expression:
\[ g(x) = -(-2x + 1) = 2x - 1 \]
So, the function that represents the reflection of \( f(x) = -2x + 1 \) across the x-axis is:
\[ g(x) = 2x - 1 \]
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