STRETCHES AND COMPRESSIONS

Today in class, we learned about the Horizontal and Vertical Stretches and Compressions.

HORIZONTAL STRETCHES

y=f(bx) , where the reciprocal of b is the stretch factor.

Example: if the b value given is 2, the reciprocal will be ½.

Graph: f(x^2)

X	Y
1	1
0	0
-1	1

f(1/2x)

You multiply the “x” values by the reciprocal of 1/2 which is 2 and the “y” values don’t change, only “x” values.

X	Y
(1)(2)=2	0
(0)(2) =0	4
(-1)(2) -2	0

HORIZONTAL COMPRESSIONS

Y = f(bx), where the reciprocal of the “b” value is the compression factor. The “y” values are not

changing, because the “x” values are affected.

Example:

f(2x)

“x” values will be multiply by ½ ( reciprocal of 2)

X	Y
(1)(1/2)=1/2	0
(0)(1/2) = 0	4
(-1)(1/2) = -1/2	0

VERTICAL STRETCHES

Y= af(x), where “a” is a vertical stretch factor.

VERTICAL COMPRESSION

Y=af(x) where “a” is a vertical compression

Graph:

f(x) = x^3

X	Y
-1	-1
0	0
1	1

2f(x)

“x” values will be multiplied by 2 to get the “y values”

“x” values stay the same only “y” values are affected.

X	Y
-1	(-1)(2) = -2
0	(0)(2)= 0
1	(1)(2) = 2

**Order of Transformations**

1. Stretches/ compressions and reflections

2. Translations