Subjects algebra

Function Rotation 6304F6

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1. The problem states that the function $f(x) = 52x - 33$ is rotated clockwise, and we need to find a possible equation for the transformed function $g(x)$. 2. When a linear function $y = mx + b$ is rotated clockwise by 90 degrees about the origin, the slope $m$ transforms to $-\frac{1}{m}$, and the intercept changes accordingly. 3. The original slope is $m = 52$. 4. The new slope after a 90-degree clockwise rotation is: $$m' = -\frac{1}{52}$$ 5. Since none of the given options have slope $-\frac{1}{52}$, the rotation might be by 180 degrees or another angle. 6. A 180-degree rotation changes the function to: $$g(x) = -52x + 33$$ 7. Checking the options, $g(x) = -52x + 52$ is close but intercept differs. 8. The only option with slope $-52$ is $g(x) = -52x + 52$. 9. Since the intercept changed from $-33$ to $52$, this could be a vertical shift after rotation. 10. Therefore, a possible transformed function is: $$g(x) = -52x + 52$$