1. Horizontal Stretches and Compression
Lesson 5.4

2. Manipulating a Function
Given the function for the Y= screen y1(x) = 0.1(x3 – 9x2)
Use window -10 < x < 10 and -20 < y < 20
Now do the transformation
y2(x) = y1(.5x)
y3(x) = y1(3x)
Set the styles different
Make predictions for what will happen

3. Manipulating a Function
f(3x)
compressed
f(0.5x)
stretched
Original f(x)
For
Horizontal stretch
Horizontal compression
0 < a < 1
a > 1

4. Note Science Illustration on the Web
Changes to a Graph
Consider once again the effect of modifiers
For this lesson we are concentrating on b
b => horizontal stretch/compression
b > 1 causes compression
|b| < 1 causes stretching
Note Science Illustration on the Web

5. Changes to a Table Try these functions
y1(x) = 3x2 – 2x
y2(x) = y1(0.5 x)
y3(x) = y1(2x)
Go to tables (Y), then setup, F2
Table start = - 4
Table increment = 1

6. Changes to a Table Note the results f(x) f(0.5x) f(2x) Compressed
Stretched

7. Changes to a Graph View the different versions of the altered graphs
What has changed?
What remains the same?

8. Changes to a Graph
Classify the following properties as changed or not changed when the function f(x) is modified by a coefficient    f(b*x)
Property
Changed
Not Changed
Zeros of the function
Intervals where the function increases or decreases
X locations of the max and min
Y-locations of the max and min
Steepness of curves where function is increasing/decreasing

9. Functions Where Formula Not Known
Given a function defined by a table
Fill in all possible blanks x -3 -2 -1 1 2 3
f(x) -4 -6
f(.5x)
f(2x)

10. Functions Where Formula Not Known
Given f(x) defined by graph below
Which is f(2x)? 2*f(x)? f(0.5x)?

11. Assignment
Lesson 5.4
Page 223
Exercises 1 – 27 odd