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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

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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 • About the Y-axis: • About the X-axis:**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 Yes, about y • 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

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