Activity 5.3 Vertical Stretches and Compressions
Overview:
Students are given a table of values for a function and asked to complete the table with values of
stretches and compressions. They are then asked to graph the original function and compare it
to the transformed functions’ graphs and to describe the relationship between the original
function’s graph and the transformed functions’ graphs.
The final question of the activity asks students to describe transformed function that include each
of the transformations discuss in 5.1, 5.2 and 5.3.
Estimated Time Required:
The activity should take approximately 15 minutes.
Technology: None
Prerequisite Concepts:

Vertical and horizontal shifts and reflections
Discussion:
Pay particular attention to the points that have zero as the y-coordinate when stretching or
compressing. Because these points are unchanged, not that the graph of g = 2f(x) is obtained
from the graph of f by stretching away from the x-axis and the 2 is called a stretch factor. Note
that it is important to work with examples that have x-intercepts because examples that do not
cross the x-axis appear to move away from the x-axis during the transformation, which may lead
to student confusion between vertical stretches and vertical shifts. When examples have points
that stay put, much of the confusion can be avoided.
Activity 5.3 Vertical Stretches and Compressions
1. Fill in the values in the table:
x
-3
-2
3
8
9
f(x)
-1
0
5
0
-1
2 f(x)
1
f x
2
By the way, f(x) = 5 – | x – 3 |.
2. Graph f, g(x) = 2 f(x) and h(x) =
1
f  x  on the same set of axes.
2
3. Describe the relationship between f and g.
Between f and h.
4. If you know the graph of f, describe how to get the graph of each of the following functions
from the graph of f.
f  x  4
f  x  6
f  x  3
f  x
 f  x
f  x  2  1
2 f  x  3
1
f x  2
3
 f  x  4
 f  x  4
2 f  x  4