Function Transformations

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# Function Transformations - PowerPoint PPT Presentation

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

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## PowerPoint Slideshow about 'Function Transformations' - dysis

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### Function Transformations

Lecture: 2CPre 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

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

Homework Review

Function is increasing without concavity

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

Homework Review

Function is Increasing & Concave Up

Because 2nd Diff is Constant, Function is Quadratic

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

Example
• Let’s use origin as reference for shifts
• No, Vertical Shift
• No, Horizontal Shift
• Flip

• VStretch: (1,1) →(-4,1)
• Stretch: (1,1) →(2,1)
• New to Old so ½

↑New Original↓

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