x2 t07 02 transformations (2012)
TRANSCRIPT
![Page 1: X2 t07 02 transformations (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/1.jpg)
(C) Transformations
![Page 2: X2 t07 02 transformations (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/2.jpg)
(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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/3.jpg)
(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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/4.jpg)
(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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/5.jpg)
(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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/6.jpg)
(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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/7.jpg)
(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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/8.jpg)
xfy (reflect f(x) in the x axis)
![Page 9: X2 t07 02 transformations (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/9.jpg)
xfy (reflect f(x) in the x axis)
y
x
y=f(x)
![Page 10: X2 t07 02 transformations (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/10.jpg)
xfy (reflect f(x) in the x axis)
y
x
y=f(x)
xfy
![Page 11: X2 t07 02 transformations (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/11.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/12.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/13.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/14.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/15.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/16.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/17.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/18.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/19.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/20.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/21.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/22.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/23.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/24.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/25.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/26.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/27.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/28.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/29.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/30.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/31.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/32.jpg)
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 (2012)](https://reader033.vdocuments.mx/reader033/viewer/2022052901/556f5e60d8b42a916b8b5100/html5/thumbnails/33.jpg)
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)