1. (C) Transformations

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)