2.6: Absolute Value and Families of Functions

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Presentation transcript:

2.6: Absolute Value and Families of Functions Our feelings are our most genuine paths to knowledge.

Absolute Value Ex1) Graph y = |x|

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 by a value between 0 and 1 Reflection: Change y values to their opposites when reflecting over the x-axis

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

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

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

2.6: Absolute Value and Families of Functions HW: 1-13 odd, 17-27 odd, 30-34 even, 35-37 all Our feelings are our most genuine paths to knowledge.