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Combining several transformations The order is very important

Combining several transformations The order is very important This power point will demonstrate which order to do them in This will then be applied to a Sine Curve. Y= x 2. Y= (2x) 2. Horizontal stretch factor ½ HIVO HOVIS Horizontal In side – Horizontal Opposite. Y= (x–3) 2.

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Combining several transformations The order is very important

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  1. Combining several transformations The order is very important This power point will demonstrate which order to do them in This will then be applied to a Sine Curve

  2. Y= x2

  3. Y= (2x)2 Horizontal stretch factor ½ HIVO HOVIS Horizontal In side – Horizontal Opposite

  4. Y= (x–3)2 Horizontal translation +3 HIVO HOVIS Horizontal In side – Horizontal Opposite

  5. More Combined Transformations f(x) = (2x – 1)2 f(x) = (x–1)2 f(x) = (x)2 Step 1 Horizontal translation +1

  6. More Combined Transformations f(x) = (2x–1)2 f(x) = (2x – 1)2 f(x) = (x–1)2 Step 2 Horizontal stretch factor ½ All x values are ½ their original value X intercept at x = ½ as expected if 2x–1 = 0 then x = ½

  7. Y= (2x–3)2 Horizontal translation +3 Horizontal stretch factor ½

  8. So the order is: • Translate horizontally left or right • Stretch horizontally • Stretch Vertically • Translate vertically HIVO Horizontal Inside Vertical Outside HOVIS Horizontal Opposite Vertical Is Same

  9. Trig Transformations y y=sint t We need to sketch the graph of y = 3sin(5t+90)+2

  10. Trig Transformations y period = 360 y=sint t Crosses x axis at 0, 180, 360, 540

  11. Trig Transformations y Translate horizontally left or right y=sin(t+90) t Horizontal translation of -90 Inside = horizontal opposite Crosses x axis at 90, 270, 450

  12. Wave frequency = 5 Period = = 72 72 Trig Transformations y y=sin(5t+90) t Stretch horizontally Horizontal stretch of  Inside = horizontal opposite Crosses x axis at 18, 54, 90

  13. Trig Transformations y Stretch Vertically y=3sin(5t+90) t Vertical stretch of factor 3 Outside = vertical same

  14. Trig Transformations y y=3sin(5t+90)+2 t +2 Vertical translation of +2 Outside = vertical same

  15. Sketch the graph of • y = 1sin(t + 45) • y = 2sin(t + 30) • y = 3sin(2t – 90) • y = 4sin(3t + 60)

  16. 1 2 3 4 y = 2sin(t + 30) y = 1sin(t + 45) Translate horizontally by –30Stretch vertically factor of 2 Translate horizontally by –45 y = 3sin(2t – 90) y = 4sin(3t + 60) Translate by horizontally–60Stretch horizontally by 1/3Stretch vertically factor of 4 Translate horizontallyby +90Stretch horizontally by ½ Stretch vertically factor of 3

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