1. Exercise #8
Horizontal and Vertical Stretches
2 f ( x) f (2 x)
f ( x) x2
Example
The graph below is f ( x) .
y
x
x
Sketch 3 f ( x) Sketch f
3
y y
x x

2. Generalizations
f ( x) af ( x)
f ( x) f (b( x))
Combining translations and stretches
** Always stretch first, then translate around the graph!
Putting Transformations Together
f ( x)
y
x
1
Sketch 2 f ( x 3) 2 Sketch f x
2
y y
x x
Journal The x-intercepts of f(x) are 6, 2 and –8. Determine the x-intercepts of f(2x – 4).