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 Using Stretches or Compressions

Graphing Using Stretches or Compressions

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

Reflection about the x-axis

Reflection about the x-axis

Reflection about the y-axis

Reflection about the y-axis

Summary of Graphing Techniques

Summary of Graphing Techniques

Summary of Graphing Techniques

Determining the Function from a Series of Transformations

Determine the Function

Combining Graphing Procedures

Combining Graphing Procedures