Apply rules for transformations by graphing absolute value functions.

Absolute Value Function  V-shaped graph that opens up or down Up when positive, down when negative  Parent function: y = |x|  Axis of symmetry is the vertical axis through the middle of the graph.  Has a single maximum point OR minimum point called the vertex.

Translation  Shift of a graph horizontally, vertically, or both.  Same size and shape, different position

Try it.  Create a table and sketch the graph of the following:  y = |x| + 2  y = |x| - 3  What do you notice?

Vertical Translation  Start with the graph of y = |x|  y = |x| + b translates the graph up  y = |x| - b translates the graph down

Try this.  Create a table and sketch the graph of the following:  y = |x + 3|  y = |x – 1|  What do you notice?

Horizontal Translation  Start with the graph of y = |x|  y = |x + h| translates the graph to the left  y = |x – h| translates the graph to the right.

Vertical Stretch and Compression

General Form

Writing Absolute Value Functions

Assignment  Odds p.111 #13-33