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6.4 Absolute-Value Functions

6.4 Absolute-Value Functions. Objectives: Explore features of the absolute-value function. Explore basic transformations of the absolute-value function .

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6.4 Absolute-Value Functions

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  1. 6.4 Absolute-Value Functions Objectives: Explore features of the absolute-value function. Explore basic transformations of the absolute-value function. Standards Addressed: 2.8.11.O: Determine the domain and range of a relation. 2.8.11.Q: Represent functional relationship in tables, charts, and graphs.

  2. The first coordinates in the set of ordered pairs are the domain of the relation, and the second coordinates are the range of the relation.

  3. Ex. 1

  4. Ex. 2 Find the domain and range of each function. Then graph each function. • A. Domain All Reals Range y > 0

  5. b. Y = I7xI • Domain All Reals • Range y > 0

  6. c. Y = Ix – 4I • Domain all real numbers • Range y > o

  7. D. Y = IxI -4 • Domain all real #s • Range y > 4

  8. Types of Transformations:

  9. Types of Transformations:

  10. Ex. 3

  11. C. Y = - IxI - 4 • Reflect x axis • Vertical Translation down 4

  12. D. Y = Ix – 10I + 2 • Horizontal Translation Right 10 • Vertical Translation up 2

  13. E. Y = I6x – 1I • Horizontal Compression 1/6 • Horizontal Translation Right

  14. F. Y = -3IxI • Reflection x axis • Vertical Stretch 3

  15. 2.What happens to the graph of the function y = IxIwhen it is reflected through the y-axis verse the x-axis? • 3.How does the graph of y = 3IxI compare with the graph of y = IxI?

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