x2 t07 02 transformations (2011)

(C) Transformations

(C) TransformationsGiven that the graph y = f(x) can be sketches, then it is possible to build other sketches through appropriate transformations.

(C) TransformationsGiven that the graph y = f(x) can be sketches, then it is possible to build other sketches through appropriate transformations.

axfy (a is grouped with y: shift up or down by a)

xfayOR

(C) TransformationsGiven that the graph y = f(x) can be sketches, then it is possible to build other sketches through appropriate transformations.

axfy (a is grouped with y: shift up or down by a)

xfayOR

y

x

y=f(x)

(C) TransformationsGiven that the graph y = f(x) can be sketches, then it is possible to build other sketches through appropriate transformations.

axfy (a is grouped with y: shift up or down by a)

xfayOR

y

x

y=f(x)a

a

a

a

axfy

(C) TransformationsGiven that the graph y = f(x) can be sketches, then it is possible to build other sketches through appropriate transformations.

axfy (a is grouped with y: shift up or down by a)

xfayOR

axfy (a is grouped with x: shift left or right by a)y

x

y=f(x)a

a

a

a

axfy

(C) TransformationsGiven that the graph y = f(x) can be sketches, then it is possible to build other sketches through appropriate transformations.

axfy (a is grouped with y: shift up or down by a)

xfayOR

axfy (a is grouped with x: shift left or right by a)y

x

y=f(x)a

a

a

a

axfy

b

b

b

b

b

bxfy

xfy (reflect f(x) in the x axis)

xfy (reflect f(x) in the x axis)

y

x

y=f(x)

xfy (reflect f(x) in the x axis)

y

x

y=f(x)

xfy

xfy (reflect f(x) in the x axis)

y

x

y=f(x)

xfy

xfy (reflect f(x) in the y axis)

xfy (reflect f(x) in the x axis)

y

x

y=f(x)

xfy

xfy (reflect f(x) in the y axis)

xfy (reflect f(x) in the x axis)

y

x

y=f(x)

xfy

xfy (reflect f(x) in the y axis)

xfy

xfy (reflect f(x) in the x axis)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy (reflect f(x) in the x axis)

y

x

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy

xfy (reflect f(x) in the x axis)

y

x

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy

xfy (reflect f(x) in the x axis)

y

x

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy

xfy (reflect f(x) in the x axis)

y

x

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy

xfy (reflect f(x) in the x axis)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy (reflect the part of f(x) where x>0 in the y axis)

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xfy (reflect f(x) in the x axis)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy (reflect the part of f(x) where x>0 in the y axis)

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper)

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper)

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

1, kxkfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper)

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

1, kxkfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper)

1, kxkfy

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

1, kxkfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper)

1, kxkfy

Note:•domain remains same•x intercepts remain same

xfy (reflect f(x) in the x axis)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy (reflect the part of f(x) where x>0 in the y axis)

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper) kxfy (stretch f(x) horizontally, k<1 shallower,k>1 steeper)

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper) kxfy (stretch f(x) horizontally, k<1 shallower,k>1 steeper)

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

1, kkxfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper) kxfy (stretch f(x) horizontally, k<1 shallower,k>1 steeper)

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

1, kkxfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper)

1, kkxfy

kxfy (stretch f(x) horizontally, k<1 shallower,k>1 steeper)

xfy (reflect f(x) in the x axis)

y=f(x)

xfy (reflect f(x) in the y axis)

xfy (reflect the part of f(x) where f(x)<0 in the x axis)

1, kkxfy

xfy (reflect the part of f(x) where x>0 in the y axis)

y

x

xkfy (stretch f(x) vertically, k<1 shallower,k>1 steeper)

1, kkxfyNote:•range remains same•y intercepts remain same

kxfy (stretch f(x) horizontally, k<1 shallower,k>1 steeper)