NORTH HUNTERDON HIGH SCHOOL
PRECALCULUS I
TEACHER: MRS. PARZIALE
LESSON GUIDE – THE GRAPH SCALE-CHANGE THEOREM
CHAPTER 3 – LESSON 5
Vocabulary:
Vertical stretch:
Horizontal stretch:
Scale change:
Vertical scale change:
Horizontal scale change:
Size change:
Example 1:
Consider the graph of y = x3 − 4 x
(a) Graph. Complete the table and graph on the grid:
x
y
-2
-1
0
1
2
(b) Replace (y) with
y
.
3
Solve the new equation for y: _________________________. Graph it on the same grid above.
What happens to the y-coordinates? __________________
This is called a ______________________________ of magnitude ______.
Under what scale change is the new figure a size change of the original? _______
(c) Replace (x) with
x
.
2
Solve the new equation for y: _________________________. Graph it.
Page 1 of 3
NORTH HUNTERDON HIGH SCHOOL
PRECALCULUS I
TEACHER: MRS. PARZIALE
LESSON GUIDE – THE GRAPH SCALE-CHANGE THEOREM
CHAPTER 3 – LESSON 5
What happens to the x-coordinates? __________________
This is called a _________________________________ of magnitude ______.
Under what scale change is the new figure a size change of the original? _______
(d) Let f ( x) = x3 − 4 x . Find an equation for g(x), the image of f(x) under S ( x, y ) → (2 x,3 y ) .
First – look at the next theorem:
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 ________________________________.
Now, write the equation of the transformed function.
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NORTH HUNTERDON HIGH SCHOOL
PRECALCULUS I
TEACHER: MRS. PARZIALE
LESSON GUIDE – THE GRAPH SCALE-CHANGE THEOREM
CHAPTER 3 – LESSON 5
x

Example 2: Consider y = x . Find an equation for the function under S ( x, y ) →  , −2 y 
3


x

Consider y = x under the scale change S ( x, y ) →  , −2 y 
3

Describe what happens to all of the x values:
Describe what happens to all of the y values:
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):
x
Example 3: The graph to the right is y = f(x). Draw 3 y = f ( ) .
4
What should happen to all of the x values?
What should happen to all of the y values?
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