1. 2.6: Absolute Value and Families of Functions

2. Absolute Value Ex1) Graph y = |x|

3. Terms Family of Functions: Functions with certain common characteristics. (ex: the absolute value functions) Parent Function: Simplest function with these characteristics Translation: Shift horizontally, vertically, or both Stretch: occurs when multiplying the function by a value greater than 1 Shrink: occurs when multiplying the function be a value between 0 and 1 Reflection: Change y values to their opposites when reflecting of the x axis

4. Transformations (the whole enchilada) #2: horizontal translation (opposite) #3: vertical translation #1: vertical stretch (|a| > 1) or shrink (0 < |a| < 1) *negative: vertical reflection Parent function y = |x| Key points (-1, 1), (0, 0), (1, 1)

5. Describe Describe, in order, the sequence of transformations of each function and then graph the function by hand.

6. Write the Function Write a function rule for each of the graphs below.