Transformation of Graphs

Andrew Robertson

Transformation of f(x)+a

f(x) = x2

Transformation of f(x)+a

y = x2 + 3

Transformation of f(x)+s

y = x2 - 2

Transformation of sf(x)

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

2f(x)

Transformation of sf(x)

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

0.5f(x)

Transformation of sf(x)

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

Transformation of f(x+s)

f(x) = x2

f(x-2)

Transformation of f(x+s)

y=f(x-2) = (x-2)2

f(x+2)

Transformation of f(x+s)

y=f(x+2) = (x+2)2

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

f(2x)

Transformation of f(sx)

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

f(0.5x)

Transformation of f(sx)

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

-f(x)

Transformation of -f(x)

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

-f(x)

Transformation of -f(x)

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

f(-x)

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

Combinations of transformations

f(x)= x2 then y=f(x+2)-3 = (x+2)2 -3

Combinations of transformations

• y = x2 then y=-2f(x-3) = -2(x-3)2

F(αx±β) - Inside brackets always effects the horizontal

αF(x) ±β - Outside brackets always effects the vertical

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)