FST
Notes for Lesson 3-5 The Graph Scale-Change Theorem
In order to understand the effect of a scale change on the equation of a
function, it is important to do the In-class activity on page 186 first. This is
because we DID NOT get to scale changes in Algebra II last year. You must
first come up to speed by observing graphs and tables. Record your answers
here:
Start with Divide y by 3:
y1  x3  4 x y2
 x3  4 x
3
Graph it.
Is it odd
or even?
Solve for y2
y2 =_______
Graph y1 & y2
Look at the
table starting
at x  3
y-coords are mult
by ______
This is a ______
_____________
______________


Multiply y by Divide x by 2:
3
5
 x
 x
y4     4  
5 y3  x 3  4 x
 2
 2
Multiply x by 3:
Solve for y3
Graph y1 & y5
Graph y1 & y4
y3 =_______ Look at the
Graph y1 & y3 table starting
at x  6
Look at the
y5  (3x)3  4(3x)
Look at the
table starting
at x  6
For what value of
x is y1  15?
For what value of
x is y1  192?
For what value of
x is y2  15?
For what value of
x is y2  192?
This is a ____
x-coords are mult
by _____
x-coords are mult
by ______
___________
This is a _______
This is a _______
___________
______________
______________
______________
______________
table.
y-coords are
multiplied by
_____
In general, if you begin with an arbitrary function y  f ( x) , and
y
you replace y by
you get ______________________________
b
In general, if you begin with an arbitrary function y  f ( x) and
x
you replace x by you get ______________________________
a
FST
The Graph Scale-Change Theorem says that there are two actions that
yield the same graph:
x
y
1. Replacing y with
and replacing x with
in the equation of a
a
b
relation
2. Applying the scale change ( x, y )  (ax, by ) to the graph of the
original relation.
Examples:
1. Graph y  x3 and its image under the scale-change  x, y    2 x, y  .
Write the equation of the image. Describe the symmetry of the
original function and the symmetry of the image.
y
x
 y
2. Graph y  x 2  2 x and its image under the scale change ( x, y )   x,  .
 2
Write the equation of the image. Describe the symmetry of the
original function and the symmetry of the image.
y
x