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Chapter 2

Chapter 2. Functions and Their Graphs. Section 5 Graphing Techniques: Transformations. 1 st : Identify the basic function, what is happening with x X 2 √x x 3 3 √x 1/x 2 nd : Determine starting ordered pairs X 2 √x x 3 3 √x 1/x. 3 rd : Identify the transformations

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Chapter 2

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  1. Chapter 2 Functions and Their Graphs

  2. Section 5Graphing Techniques: Transformations

  3. 1st: Identify the basic function, what is happening with x X2 √x x33√x 1/x 2nd: Determine starting ordered pairs X2 √x x33√x 1/x

  4. 3rd: Identify the transformations 1) Add/subtract directly to x, horizontal shift left/right respectively (add/subtract value directly to x) y = f(x + h)  left; y = f(x – h)  right 3) Add/subtract to overall function, vertical shift up/down respectively (add/subtract value directly to y) y = f(x) + k  up; y = f(x) – k  down 2) Multiplying overall function, vertical stretch/compression and/or reflection (multiply to y-value) (#>1) (0<#<1) (-)# y = af(x) *NOTE: Recommended order of transformations: (1) Horizontal Translation, (2) Horizontal Stretch (3) Horizontal Reflection (4) Vertical Reflection (5) Vertical Stretch, (5) Vertical Translation

  5. Example 5: Basic:

  6. Example: f(x) = -2|x + 1| - 3 Basic:

  7. Example: Write the equation of the function whose graph is y = x3 but is a) shifted up 2 units b) shifted right by 1 c) vertically stretched by 3

  8. EXIT SLIP

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