To determine what kind of transformation converts the graph of \( f(x) = -4x + 9 \) into \( g(x) = 4x + 9 \), we need to analyze the two functions.
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Reflection across the y-axis: This would change \( f(x) = -4x + 9 \) to \( f(-x) = 4x + 9 \), which is exactly \( g(x) \). Therefore, this transformation works.
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Horizontal stretch: A horizontal stretch would change the x-coefficients without affecting the sign change necessary here.
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Horizontal shrink: Like horizontal stretch, this modification wouldn't convert \( -4x \) to \( 4x \).
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Reflection across the x-axis: This transformation would change \( f(x) \) to \( -f(x) = 4x - 9 \), which does not produce \( g(x) \).
The correct transformation is reflection across the y-axis.