x2 t07 02 transformations (2011)

33
(C) Transformations

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Page 1: X2 T07 02 transformations (2011)

(C) Transformations

Page 2: X2 T07 02 transformations (2011)

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

Page 3: X2 T07 02 transformations (2011)

(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

Page 4: X2 T07 02 transformations (2011)

(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)

Page 5: X2 T07 02 transformations (2011)

(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

Page 6: X2 T07 02 transformations (2011)

(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

Page 7: X2 T07 02 transformations (2011)

(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

Page 8: X2 T07 02 transformations (2011)

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

Page 9: X2 T07 02 transformations (2011)

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

y

x

y=f(x)

Page 10: X2 T07 02 transformations (2011)

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

y

x

y=f(x)

xfy

Page 11: X2 T07 02 transformations (2011)

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

y

x

y=f(x)

xfy

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

Page 12: X2 T07 02 transformations (2011)

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

y

x

y=f(x)

xfy

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

Page 13: X2 T07 02 transformations (2011)

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

y

x

y=f(x)

xfy

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

xfy

Page 14: X2 T07 02 transformations (2011)

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)

Page 15: X2 T07 02 transformations (2011)

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

Page 16: X2 T07 02 transformations (2011)

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

Page 17: X2 T07 02 transformations (2011)

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

Page 18: X2 T07 02 transformations (2011)

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

Page 19: X2 T07 02 transformations (2011)

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)

Page 20: X2 T07 02 transformations (2011)

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

Page 21: X2 T07 02 transformations (2011)

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

Page 22: X2 T07 02 transformations (2011)

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

Page 23: X2 T07 02 transformations (2011)

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

Page 24: X2 T07 02 transformations (2011)

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)

Page 25: X2 T07 02 transformations (2011)

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)

Page 26: X2 T07 02 transformations (2011)

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)

Page 27: X2 T07 02 transformations (2011)

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

Page 28: X2 T07 02 transformations (2011)

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

Page 29: X2 T07 02 transformations (2011)

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)

Page 30: X2 T07 02 transformations (2011)

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)

Page 31: X2 T07 02 transformations (2011)

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)

Page 32: X2 T07 02 transformations (2011)

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)

Page 33: X2 T07 02 transformations (2011)

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)