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X2 t07 02 transformations (2013)

N
Nigel Simmons

The document describes various transformations that can be applied to a graph y=f(x) to generate other graphs. These transformations include: shifting the graph up or down by adding or subtracting a constant a; stretching or compressing the graph vertically by multiplying y by a constant k; reflecting parts or all of the graph across the x-axis or y-axis; and stretching or compressing the graph horizontally by multiplying x by a constant k. Combinations of these transformations can be used to transform the original graph in various ways.

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

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X2 t07 02 transformations (2013)

  • 2. (C) Transformations Given that the graph y = f(x) can be sketches, then it is possible to build other sketches through appropriate transformations.
  • 3. (C) Transformations Given 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 
  • 4. (C) Transformations Given 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)
  • 5. (C) Transformations Given 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 
  • 6. (C) Transformations Given 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 
  • 7. (C) Transformations Given 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 
  • 8.  xfy  (reflect f(x) in the x axis)
  • 9.  xfy  (reflect f(x) in the x axis) y x y=f(x)
  • 10.  xfy  (reflect f(x) in the x axis) y x y=f(x)  xfy 
  • 11.  xfy  (reflect f(x) in the x axis) y x y=f(x)  xfy   xfy  (reflect f(x) in the y axis)
  • 12.  xfy  (reflect f(x) in the x axis) y x y=f(x)  xfy   xfy  (reflect f(x) in the y axis)
  • 13.  xfy  (reflect f(x) in the x axis) y x y=f(x)  xfy   xfy  (reflect f(x) in the y axis)  xfy 
  • 14.  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)
  • 15.  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 
  • 16.  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 
  • 17.  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 
  • 18.  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 
  • 19.  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)
  • 20.  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
  • 21.  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
  • 22.  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
  • 23.  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
  • 24.  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)
  • 25.  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)
  • 26.  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)
  • 27.  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
  • 28.  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
  • 29.  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)
  • 30.  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)
  • 31.  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)
  • 32.  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)
  • 33.  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)