1. Families of Functions Objective: I can understand transformations of functions. Write in your notebook ONLY what you see in the yellow boxes [except for this yellow box ]. Everything will be done on your graphing calculator today.

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 Translations Vertical Translation: k units Up:Down: xy1y1 y2y2 003 114 247 3912

4. Graph Translations Horizontal Translation, h units Left:Right: xy1y1 y2y2 009 114 241 390 4161 5254

5. Reflections Graph Reflections: Across x-axis Across y-axis xy1y1 y2y2 000 11 21.4-1.4 31.7-1.7 xy1y1 y3y3 -2error1.4 error1 000 11 21.4error

6. Dilations: Vertical stretchcompression Dilations Graph xy1y1 y2y2 -224 12 000 112 224

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

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