The Graph Scale-Change
Theorem
SECTION 3.5
y=x2
y = 2x2
Graph Scale-Change Theorem
 A scale change centered at the origin with a
horizontal factor a ≠ 0 and a vertical scale factor b ≠
0 is a transformation that maps (x,y) to (ax, by)
 S(x,y)  (ax, by)
 In the equation, it should be
 Just like Graph Translations!
Example 1
 1. Compare the graphs of y = |x| and y = |6x|
 The second is has a horizontal scale change of
magnitude 1/6.
Example 2:
 Sketch the graph of
 Vertical scale of
magnitude 4, horizontal
change of 1/6
 Some points are:
 (0,0) , (1,24) , (-1,24)
Example 3
 Sketch the image of y = x3 under S(x,y) = (-2x, y)
y = (-x/2)3
 Vertical scale of
magnitude 0, horizontal
change of 2
 Some points are:
 (0,0) , (-2,1) , (4, -8)
Example 4
 The line 41x – 29y = 700 contains the points (39,31)
and (10,-10). Use this information to obtain two
points on the line with equation 20.5x – 87y = 700
 x is reduced by ½ in the equation.
 y is multiplied by 3 in the equation.
 Horizontal change: 2
 Vertical change: 1/3
 So s(x,y)  (2x, 1/3y)
 (20, -10/3) and (78, 31/3)
Homework
Pages 191 – 193
3, 5, 7-9,
14-16, 20