Solving Absolute Value Inequalities October 8, 2015 SWBAT: Solve Absolute Value Inequalities.
2.6: Absolute Value and Families of Functions. Absolute Value Ex1) Graph y = |x|
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Transcript of 2.6: Absolute Value and Families of Functions. Absolute Value Ex1) Graph y = |x|
2.6: Absolute Value and Families of Functions
Absolute ValueEx1) Graph y = |x|
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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
Transformations (the whole enchilada)
khxay #2: horizontal
translation (opposite)
#3: vertical translation
#1: vertical stretch (|a| > 1) or shrink (0 < |a| < 1)
*negative: vertical reflection
-5 -4 -3 -2 -1 1 2 3 4 5
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Parent function y = |x|
Key points (-1, 1), (0, 0), (1, 1)
Describe
-5 -4 -3 -2 -1 1 2 3 4 5
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Describe, in order, the sequence of transformations of each function and then graph the function by hand.
1) ( ) 3 4f x x 2) ( ) 3 2f x x 1
3) ( ) 2 12
f x x
-5 -4 -3 -2 -1 1 2 3 4 5
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-5 -4 -3 -2 -1 1 2 3 4 5
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Write the Function
-5 -4 -3 -2 -1 1 2 3 4 5
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-5 -4 -3 -2 -1 1 2 3 4 5
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-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
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Write a function rule for each of the graphs below.