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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

Function Transformations

Lecture: 2CPre AP & GT Precalculus

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

Function is decreasing without concavity

Function is linear and has algebraic form (not required):

homework review4
Homework Review

Function is increasing without concavity

Function is linear and has algebraic form (not required):

homework review5
Homework Review

Function is Increasing & Concave Up

Because 2nd Diff is Constant, Function is Quadratic

vertical shift
Vertical Shift
  • Rigid Transformation
horizontal shift
Horizontal Shift
  • Rigid Transformation
flips
Flips
  • Rigid Transformation
  • About the Y-axis:
  • About the X-axis:
horizontal shrinks stretches
HorizontalShrinks & Stretches
  • Non-Rigid Transformation
vertical shrinks stretches
VerticalShrinks & Stretches
  • Non-Rigid Transformation
  • c f(x)
  • If c>1 stretch
  • If c<1 shrink
examples
Examples
  • 13 units to the left:
  • 2 to the right and 8 down:
    • _
      • 10 up, reflected about x-axis:
        • _
example
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↓

example13
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↓

example14
Example
  • Parent Function:

Absolute Value

  • Hshift:

NO

  • Vshift:

Yes, Down 2

  • VStretch:

(2,2) →(2,-1)→(2,1), +2

  • Flip:

Yes, x

↑New Original↓

what does it mean
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)
homework
Homework
  • Pg 80 V6, #13-18 (A) Pg 81 #44-50 (even)Pg 83 #69,70,73