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Transformation of Functions Section 1.6

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Objectives Describe a transformed function given by an equation in words. Given a transformed common function, write the transformed function's equation.

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Vocabulary common function horizontal shift vertical shift vertical stretch/shrink reflect over the x-axis reflect over the y-axis

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Common Functions

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Graph the functions and In general: Vertical shift up by c units

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Graph the functions and In general: Horizontal shift left by c units

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Graph the functions and In general: Vertical shift down by c units

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Graph the functions and In general: Horizontal shift right by c units

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Shift Summary Vertical shifts Horizontal shift Vertical shift up by c units Vertical shift down by c units Horizontal shift left by c units Horizontal shift right by c units

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Graph the functions and In general: Reflect over x-axis

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Graph the functions and In general: Reflect over y-axis

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Graph the functions and In general: Vertical stretch away from x-axis by a factor of c

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Graph the functions and In general: Vertical shrink toward x-axis by a factor of c

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Graph the functions and In general: Horizontal shrink toward y-axis by a factor of 1/c

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Graph the functions and In general: Horizontal stretch away from y-axis by a factor of 1/c

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Stretch/Shrink/Reflection Summary Vertical Vertical shrink toward x-axis by a factor of c Vertical stretch away from x-axis by a factor of c Reflect over x-axis

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Stretch/Shrink/Reflection Summary Horizontal Reflect over y-axis Horizontal shrink toward y-axis by a factor of 1/c Horizontal stretch away from y-axis by a factor of 1/c

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Given, after performing the following transformations: shift to the left 76 units, shrink vertically by a factor of, and shift downward 13 units, write the new function.

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