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What are the math formulas for reflection in graphs and rotating angles?

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What are the math formulas for reflection in graphs and rotating angles?

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a refection in the x-axis of a function is multiplying the x values by -1, therefore they go on the opposite side of the x axis reflection in the y axis is multiplying the y values by -1 therefore they get switch reflection in the line y=x is switching the x and y of a function

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