2.6: Absolute Value and Families of Functions

Absolute ValueEx1) Graph y = |x|

-5 -4 -3 -2 -1 1 2 3 4 5

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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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-2

-1

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5

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

-5

-4

-3

-2

-1

1

2

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5

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

Write the Function

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

Write a function rule for each of the graphs below.