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Function Transformations

Function Transformations. Lecture: 2C Pre AP & GT Precalculus. Agenda. Homework Review Rigid Transformations Shifts (Vertical & Horizontal) Non-Rigid Transformations Shrinks & Stretches What does it mean?. Homework Review. Function is decreasing without concavity.

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Function Transformations

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  1. Function Transformations Lecture: 2CPre AP & GT Precalculus

  2. Agenda • Homework Review • Rigid Transformations • Shifts (Vertical & Horizontal) • Non-Rigid Transformations • Shrinks & Stretches • What does it mean?

  3. Homework Review Function is decreasing without concavity Function is linear and has algebraic form (not required):

  4. Homework Review Function is increasing without concavity Function is linear and has algebraic form (not required):

  5. Homework Review Function is Increasing & Concave Up Because 2nd Diff is Constant, Function is Quadratic

  6. Vertical Shift • Rigid Transformation

  7. Horizontal Shift • Rigid Transformation

  8. Flips • Rigid Transformation • About the Y-axis: • About the X-axis:

  9. HorizontalShrinks & Stretches • Non-Rigid Transformation

  10. VerticalShrinks & Stretches • Non-Rigid Transformation • c f(x) • If c>1 stretch • If c<1 shrink

  11. Examples • 13 units to the left: • 2 to the right and 8 down: • _ • 10 up, reflected about x-axis: • _

  12. Example • Let’s use origin as reference for shifts • No, Vertical Shift • No, Horizontal Shift • (1,0) →(2,0) • With same y-values what do we do to get from new to old • From 2 to 1 multiply by ½ • So HStretch of one-half ↑New Original↓

  13. Example • Let’s use origin as reference for shifts • No, Vertical Shift • No, Horizontal Shift • Flip Yes, about y • VStretch: (1,1) →(-4,1) • Stretch: (1,1) →(2,1) • New to Old so ½ ↑New Original↓

  14. Example • Parent Function: Absolute Value • Hshift: NO • Vshift: Yes, Down 2 • VStretch: (2,2) →(2,-1)→(2,1), +2 • Flip: Yes, x ↑New Original↓

  15. What does it mean? • I wanted to paint my house and bought F(x) gallons • Which transformation corresponds to: • I bought two extra gallons just in case: • F(x) +2 • I bought enough paint to cover my house twice: • 2 F(x) • I bought enough paint for my house plus my mailbox which is 2 square feet: • F(x+2)

  16. Homework • Pg 80 V6, #13-18 (A) Pg 81 #44-50 (even)Pg 83 #69,70,73

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