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(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)