Sketching Graphs of FUNctions
(Transformations Recap)
The graph of y = f(x) can be transformed as follows:
y = a f( k(x – d) ) + c
 vertical stretch
(|a| > 1)
 vertical compression
(0 < |a| < 1)
 reflection (x-axis)
(a < 0)
 horizontal translation
(+) move left
(–) move right
 vertical translation
(+) move up
(–) move down
 horizontal compression
(|k| > 1)
 horizontal stretch
(0 < |k| < 1)
 reflection (y-axis)
(k < 0)
The transformations must be applied in the following order:
1.
2.
Horizontal and vertical stretches/compressions/reflections.
Horizontal and vertical translations.
Which transformation(s) affect the domain/range of a function?
Ex 
State the transformations defined by each of the following equations in the order
they would be applied to the parent function:
a)
y = 2x+2 – 4
c)
 1

y = 3f 
(x  5)  + 1
 4

b)
y=–
1
|x – 1| – 3
2
Ex 
a)
Ex 
a)
State the domain and range for each of the following:
y = – 2x+1 – 4
b)
y = 5 x 3 2
D=
D=
R=
R=
Determine the equation that results from the given sets of transformations:
y = f(x)
 vertical stretch by a factor of 2
 horizontal compression by a factor of
1
3
 reflection in the y-axis
 vertical translation 5 units up
b)
y = x2
 vertical compression by a factor of
1
5
 reflection in the x-axis
 horizontally translated 4 units left
 vertically translated 2 units down
c)
Ex 
Sketch the parent function and the transformed function:
1
2
y =   x 1  3
y
For the transformed function, state:
D=
R=
0
x
Interval of Increase:
Interval of Decrease:
End Behaviour: