Section 3.5 Graphing Techniques: Transformations.

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Presentation transcript:

Section 3.5 Graphing Techniques: Transformations

Graphing Functions Using Vertical and Horizontal Shifts

Example: Vertical Shift Up

Example: Vertical Shift Down

Vertical Shifts

Horizontal Shifts

Horizontal Shift to the Right

Horizontal Shift to the Left

Combining  and  Shifts

Graph Functions Using Compressions and Stretches

Vertical Stretch

Vertical Compression

Vertical Stretches or Compressions

Horizontal Stretches or Compressions

Graphing Using Stretches or Compressions

Graphing Functions Using Reflections about the x-axis and the y-axis

Reflection about the x-axis

Reflection about the y-axis

Summary of Graphing Techniques

Determining the Function from a Series of Transformations

Determine the Function

Combining Graphing Procedures