# Stretches of Functions

```Unit 3, Day 7 - Stretches of Functions
Vertical Stretching (along the y-axis)
A vertical stretch occurs when all the y-coordinates of a function are ________________ by the
same constant. The x-coordinate remains the same.
In function notation:
If y = f(x) is mapped onto y = 3f(x), this is called a &quot;____________________________&quot;.
If y = f(x) is mapped onto y = 0.5f(x), this is called a &quot;___________________________&quot;.
Let's look at y=f(x) as defined by the table of values below.
Determine:
x
7
5
3
0
-1
-4
y=f(x)
0
3
0
2
0
-2
x
7
5
3
0
-1
-4
y=3f(x)
x
7
5
3
0
-1
-4
y=0.5f(x)
In general, if the expansion factor is _____________ than 1, we say 'stretch' and if the
expansion factor is ___________ than 1, we say 'compression'.
Horizontal Stretching (along the x-axis)
A horizontal stretch occurs when all the x-coordinates of a function are ________________ by
the same constant. The y-coordinate remains the same.
Let's look at y=f(x) as defined by the table of values.
Determine:
x
-2
-1
0
1
2
3
y=f(x)
0
2
4
3
2
1
x
y=f(2x)
0
2
4
3
2
1
x
y=f(0.5x)
0
2
4
3
2
1
For non-zero values of x, each point on y = f(2x) is __________ as far from the y-axis as the
equivalent point on y = f(x).
We call this a horizontal ____________________ by a factor of ______.
For non-zero values of x, each point on y = f(0.5x) is __________ as far from the y-axis as the
equivalent point on y = f(x).
We call this a horizontal ____________________ by a factor of _______.
Combining Horizontal and Vertical Stretching
Let's look at y=f(x) as defined by the table of values below.
Determine:
x
0
2
4
6
8
y=f(x)
0
2
2
4
0
x
0
2
4
6
8
y=3f(x)
x
y=3f(0.5x)
0
6
6
12
0
Ex. 2) For each function below:
a) identify and graph the parent function
b) describe the transformations &amp; graph the transformed function
c) state the domain and range of the transformed functions
d) identify any invariant point(s)
i)
ii)
```