MCR3U1
U2L8
APPLYING A COMBINATION OF TRANSFORMATIONS
(using the Transformation Rules)
PART A ~ REVIEW OF TRANSFORMATIONS
Given the function f(x), where f represents one of the parent functions, the following
is a summary of the possible transformations:
 vertical stretch (|a| > 1)
 vertical compression (0 < |a| < 1)
 reflection (x-axis) (a < 0)
 vertical translation
(+) move up
(–) move down
𝑓(𝑥 ) = 𝑎𝑓[𝑘(𝑥 − 𝑑 )] + 𝑐
 horizontal compression (|k| > 1)
 horizontal stretch (0 < |k| < 1)
 reflection (y-axis) (k < 0)
 horizontal translation
(+) move left
(–) move right
Ex.
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?
MCR3U1
U2L8
PART B ~ EXAMPLES
Example 
a)
Example 
State the transformations defined by each of the following equations in
the order they would be applied to the parent function:
1
𝑦 = − (𝑥 + 8)2 − 1
4
b)
𝑦 = 3𝑓 [
−1
4
(𝑥 − 5)] + 3
If 𝑓(𝑥) = |𝑥|, graph the function 𝑦 = −2𝑓(𝑥 + 3) + 2.
y
x
Example 
If 𝑓(𝑥) = √𝑥, graph the function 𝑦 = 3𝑓[−12(𝑥 − 4)] − 2.
y
x
MCR3U1
U2L8
Example 
1
If (𝑥) = , graph the function 𝑦 = −𝑓(𝑥 + 2) − 3.
𝑥
y
x
Example 
Graph the function 𝑦 = (−2𝑥 + 4)2 − 1.
y
x
Place all equations in the form 𝑦 = 𝑎𝑓[𝑘(𝑥 − 𝑑)] + 𝑐 before graphing!!
Common factor the k if necessary!!
MCR3U1
U2L8
Example 
a)
State which parent function(s) remain unchanged by a reflection in:
the x–axis
Example 
a)
b)
the y–axis
State the equation that results from the given sets of transformations:
𝑦 = |𝑥|




b)
VS by a factor of 2
reflection in the y-axis
VT 5 units up
1
HC by a factor of
3
𝑦 = √𝑥




reflection in the x–axis
HT 4 units left
VT 2 units down
1
VC by a factor of
c)
HOMEWORK: p.70–73 #1, 2, 4bdf, 5c, 6, 7b, 8c, 9c,
11–13, 16–19, 20
5