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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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3.4 Graphs and Transformations

3.4 Graphs and Transformations

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