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Transformation of Graphs Andrew Robertson

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Transformation of f(x)+a f(x) = x 2

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Transformation of f(x)+a y = x 2 + 3

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Transformation of f(x)+s y = x 2 - 2

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Transformation of sf(x) f(x) = (x-2)(x-3)(x+1) 2f(x)

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Transformation of sf(x) y=2f(x) = 2(x-2)(x-3)(x+1) 0.5f(x)

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Transformation of sf(x) y=0.5f(x) = 0.5(x-2)(x-3)(x+1)

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Transformation of f(x+s) f(x) = x 2 f(x-2)

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Transformation of f(x+s) y=f(x-2) = (x-2) 2 f(x+2)

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Transformation of f(x+s) y=f(x+2) = (x+2) 2

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Transformation of f(sx) f(x) = (x-2)(x-3)(x+1) f(2x)

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Transformation of f(sx) y=f(2x) = (2x-2)(2x-3)(2x+1) f(0.5x)

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Transformation of f(sx) y=f(0.5x) = (0.5x-2)(0.5x-3)(0.5x+1) -f(x)

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Transformation of -f(x) f(x) = (x-2)(x-3)(x+1) -f(x)

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Transformation of -f(x) y=-f(x) = -[(x-2)(x-3)(x+1)] f(-x)

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Transformation of f(-x) f(x)=(x-2)(x-3)(x+1) y=f(-x)=(-x-2)(-x-3)(-x+1)

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Combinations of transformations f(x)= x 2 then y=f(x+2)-3 = (x+2) 2 -3

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Combinations of transformations y = x 2 then y=-2f(x-3) = -2(x-3) 2

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F(αx±β) - Inside brackets always effects the horizontal αF(x) ±β - Outside brackets always effects the vertical

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f(x) ± a Vertical shift (x,y) -> (x, y ± a) f(x ± a) Horizontal shift (x,y) -> (x a, y) Note that when + shift to Left and – shift to Right αf(x) Vertical Stretch/compression by factor α (x,y) -> (x, αy) f(αx) Horizontal Stretch/compression by factor 1/α (x,y) -> (x/α, y) f(-x) Refection though y axes (x,y) (-x, y) - f( x) Reflection through x axes (x,y) ( x, -y)

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1.31.3 Graphical Transformations. Quick Review What you’ll learn about Transformations Vertical and Horizontal Translations Reflections Across Axes Vertical.

1.31.3 Graphical Transformations. Quick Review What you’ll learn about Transformations Vertical and Horizontal Translations Reflections Across Axes Vertical.

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