1. Horizontal Stretches and Compression Lesson 5.4

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

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

4. 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

5. Changes to a Table Try these functions  y1(x) = 3x 2 – 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) Stretched Compressed

7. Changes to a Graph View the different versions of the altered graphs What has changed? What remains the same? 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) PropertyChanged 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-3-20123 f(x)-4230-3-6 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