College Algebra, 2013a

132 Relations and Functions
If, on the other hand, we wish to graph y = f ( 1
2 x) , we end up multiplying the x-coordinates
of the points on the graph of f by 2 which results in a horizontal scaling 10 by a factor of 2, as
demonstrated below.
5
y
(5, 5)
5
y
(10, 5)
4
3
2
(2, 3)
(4, 3)
4
3
2
(4, 3)
(8, 3)
(0, 1)
(0, 1)
1 2 3 4 5 6 7 8 9 10
y = f(x)
x
horizontal scaling by a factor of 2
−−−−−−−−−−−−−−−−−−−−→
multiply each x-coordinate by 2
1 2 3 4 5 6 7 8 9 10
y = g(x) =f ( 1
2 x)
x
We have the following theorem.
Theorem 1.6. Horizontal Scalings. Suppose f is a function and b>0. To graph y = f(bx),
divide all of the x-coordinates of the points on the graph of f by b. Wesaythegraphoff has
been horizontally scaled by a factor of 1 b .
ˆ If 0