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Families of Functions

Families of Functions. Objective: I can understand transformations of functions. Vocabulary. Parent Function Simplest form in a set of functions. Transformation : Change in the size or position of a function Translation : Moves a function horizontally or vertically Reflection:

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Families of Functions

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  1. Families of Functions Objective: I can understand transformations of functions.

  2. Vocabulary Parent Function • Simplest form in a set of functions. Transformation: • Change in the size or position of a function Translation: • Moves a function horizontally or vertically Reflection: • Reflects a function across a line of reflection Dilation: • Changes a function size

  3. Set your calculator window to: Graph Graph Graph Translations Vertical Translation: k units Up: Down:

  4. Graph Graph Graph Translations Horizontal Translation, h units Left: Right:

  5. Graph Graph Graph Reflections Reflections: Across x-axis Across y-axis

  6. Graph Graph Graph Dilations Dilations: Vertical stretchcompression

  7. Transformation of f(x) Translation: Horizontal (k > 0) Translation: Vertical (k > 0) Up k units Right h units Down k units Left h units Reflection Dilation: Vertical by a factor of a Across x-axis Stretch: Across y-axis Compression:

  8. Combining Transformations Find g(x) when f(x) is stretched by a factor of 0.5 and reflected across the y-axis. Find g(x) when f(x) is translated 3 units up. Find g(x) when f(x) is translated 2 units left. Pg. 104 #10-33

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