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Horizontal Stretches and Compression

Horizontal Stretches and Compression. Lesson 5.4. 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). Set the styles different.

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Horizontal Stretches and Compression

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  1. Horizontal Stretches and Compression Lesson 5.4

  2. Manipulating a Function • Given the function for the Y= screeny1(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. f(3x) compressed f(0.5x) stretched Original f(x) Manipulating a Function • For • Horizontal stretch • Horizontal compression 0 < a < 1 a > 1

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

  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)

  9. Functions Where Formula Not Known • Given a function defined by a table • Fill in all possible blanks

  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

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