3.5 The Graph Scale-Change Theorem
Functions, Statistics, and Trigonometry
Name: _______________________
Warm-Up: Recall what a scale-change is from geometry. Write a brief description and check with your
neighbor.
Essential Question: What is a scale change and what are the effects on our pre-image graph?
Vocabulary:
Scale Change: ________________________________________________________________
____________________________________________________________________________________
Horizontal Scale Factor: ______________________________________________________________
Vertical Scale Factor: _________________________________________________________________
Size Change: ________________________________________________________________________
** Scale changes do NOT produce congruent figures.
Graph Scale-Change Theorem:
In a relation described by a sentence in x and y, the following two processes yield the same graph:
(1) replacing x by
x
y
and y by in the equation;
a
b
(2) applying the scale change (x, y) --> (ax, by) to the graph of the original relation
€
€
Example 1: Compare the graphs of y = x and y = 6x .
€
€
Example 2: Sketch the graph of
y
= 6x .
4
€
Negative Scale Factors: _____________________________________________________________________
Which axis?
Example 3: Sketch the image of y = x3 under S(x, y) = (-2x, y).
Give an equation for the image.
Example 4: The line 41x – 29y = 700 contains the point (39, 31) and (10, -10). Use this information to obtain
two points on the line with equation 20.5x – 87y = 700.