Horizontal Stretches and Compression

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Presentation transcript:

Horizontal Stretches and Compression Lesson 5.4

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

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

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

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

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

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

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

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)

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

Assignment Lesson 5.4 Page 223 Exercises 1 – 27 odd