MCR3U1
U2L7
HORIZONTAL STRETCHES, COMPRESSIONS
and REFELCTIONS
PART A ~ INTRODUCTION
Functions of the form y = f(kx) have undergone a change in shape due
to a horizontal stretch, compression, or a reflection in the y–axis.
PART B ~ DEFINITIONS
invariant point: a point on a graph that is unchanged
by a transformation
ex. (–2, 0) and (2,0) are invariant in the given graph
PART C ~ INVESTIGATION OF FUNCTIONS OF THE FORM y = f(kx)
Sketch each of the following functions on the given grid:
 𝑦 = √𝑥
x
0
1
4
9
16
y
1
 𝑦=√ 𝑥
 𝑦 = √2𝑥
x
0
0.5
2
4.5
8
2
y
x
0
2
8
18
32
y
 𝑦 = √−𝑥
x
0
–1
–4
–9
–16
y
y
x
MCR3U1
U2L7
Which point(s) are invariant under the above transformations?
____________________
A point on 𝑦 = √2𝑥 is half the distance from the y–axis as the
equivalent point on 𝑦 = √𝑥. The mapping rule is:
____________________
1
A point on 𝑦 = √ 𝑥 is double the distance from the y–axis as the
2
equivalent point on 𝑦 = √𝑥. The mapping rule is:
____________________
A point on 𝑦 = √−𝑥 is reflected in the y–axis compared
to the equivalent point on 𝑦 = √𝑥. The mapping rule is:
____________________
PART D ~ SUMMARY
Transformation
Cases
𝑦 = 𝑓(𝑘𝑥)
|𝑘|>1
0<|𝑘|<1
Transformation
Mapping Rule
(𝒙, 𝒚) →
𝑘<0
PART E ~ EXAMPLES
Example 
Determine the equation of the transformed function:
a)
Example 
a)
𝑦 = 𝑓(3𝑥)
b)
The point (2,5) is on the graph of y = f(x). State the coordinates of the
image of this point on each of the following graphs:
b)
1
𝑦 = 𝑓( 𝑥)
2
c)
𝑦 = 𝑓(−4𝑥)
MCR3U1
U2L7
Example 
a)
In each case, sketch the parent function and the transformed function:
y
𝑦 = | 5𝑥 |
x
1
2
b) 𝑦 = ( 𝑥)
y
4
x
c)
𝑦 = √−3𝑥
y
x
HOMEWORK: p.59–60 #3, 4d, 5b, 6a, 7d, 8, 10abd, 11, 12