1. Chapter 3: Transformations of Graphs and Data
Lesson 5: The Graph Scale-Change Theorem
Mrs. Parziale

2. Vocabulary:
Vertical stretch: A scale change that makes the original graph taller or shorter
Horizontal stretch: a scale change that makes the original graph wider or skinnier.
Scale change: a stretch or shrink applied to the graph vertically or horizontally
Vertical scale change: The value that changes the vertical values of the graph.
Horizontal scale change: The value that changes the horizontal values of the graph.
Size change: When the same vertical and horizontal scale change occurs.

3. Example 1:
Consider the graph of (a) Complete the table and graph on the grid: x y -2 -1 1 2

4. (b) Replace (y) with
1. Solve the new equation for y and graph it on the same grid at right.
2. What happens to the y-coordinates?
3. This is called a vertical stretch of magnitude 3 .
4. Under what scale change is the new figure a vertical scale change of the original?

5. (c) Replace (x) with  
1. Solve the new equation for y and graph it.
2. What happens to the x-coordinates?
This is called a horizontal stretch of magnitude 2 .
Under what scale change is the new figure a horizontal scale change of the original?

6. (d) Let . Find an equation for g(x), the image of f(x) under What is happening to each part of the graph?

7. How is the x changed?
Change: horizontal stretch two times wider.
How is the y changed?
Change: vertical stretch three times the original.

8. Graph Scale-Change Theorem
In a relation described by a sentence in (x) and (y), the following two processes yield the same graph:
(1) replace (x) by and (y) by in the sentence
(2) apply the scale change __________________ to the graph of the original relation.
Note: If a = b, then you have performed a __________
size change
If a = negative, the graph has been reflected (flipped) over the y-axis
If b = negative, the graph has been reflected over the x-axis

9. So, What’s the Equation?
(d) Find an equation for g(x), the image of f(x) under x y -2 -1 3 1 -3 2 x y

11. Example 2: Consider . Find an equation for the function under
Describe what happens to all of the x values:
Describe what happens to all of the y values:

12. Find the equation for the transformed image by
Replace (x) with ______________
Replace (y) with ______________
Now make the new equation (remember to simplify to y= form):

13. Graph It!

14. Closure - Example 3: The graph to the right is y = f(x). Draw .
What should happen to all of the x values?
What should happen to all of the y values?