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Graphing Techniques: Transformations and Functions Exploration

Learn how to identify basic functions, apply transformations, and graph functions with horizontal and vertical shifts, stretches, compressions, and reflections. Practice identifying and implementing transformations with examples.

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Graphing Techniques: Transformations and Functions Exploration

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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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