To convert the graph of \( f(x) = -4x + 9 \) into the graph of \( g(x) = 4x + 9 \), we need to analyze the difference between the two functions.
The key difference between \( f(x) \) and \( g(x) \) is the sign of the coefficient of \( x \). In \( f(x) \), the coefficient is negative (-4), while in \( g(x) \), it is positive (4).
This change from negative to positive indicates that the graph of \( f(x) \) has been reflected across the x-axis to obtain \( g(x) \).
Thus, the correct transformation that converts \( f(x) = -4x + 9 \) into \( g(x) = 4x + 9 \) is:
Reflection across the x-axis.
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