In Try This 1 you explored what happened to the shape of a graph when you multiplied all of the x-coordinates of a function by a constant or when you multiplied all of the y-coordinates by a constant. The change in shape seen is called a stretch. In this lesson you will focus on stretches about the x-axis or the y-axis. When you're stretching about an axis, it is useful to think of a function in terms of the equation y = af(bx). In Try This 2 you will explore the outcomes of changing a and b for a function of this form.
Open Stretching/Reflecting y = af(bx).
Notice the point highlighted on the function that follows. This highlighted point shows where a particular point moves as you adjust a and b. The original coordinates and transformed coordinates of this point are listed at the bottom of Stretching/Reflecting y = af(bx). Make sure you pay attention to this information during Try This 2.
Value of a |
Value of b |
Coordinates of Original Point |
Coordinates of Transformed Point |
Description/Diagram of How the Point Changed |
Description/Diagram of How the Function Changed |
1 |
1 |
(4, 2) |
(4, 2) |
no change |
no change |
3 |
1 |
|
|
|
|
0.7 |
1 |
|
|
|
|
−2 |
1 |
|
|
|
|
1 |
4 |
|
|
|
|
1 |
0.5 |
|
|
|
|
1 |
−2 |
|
|
|
|
Student Choice |
|
|
|
|
|
Student Choice |
|
|
|
|
Save your work in your course folder.
With a partner or group, discuss the following questions based on the table you created in Try This 2.