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Exploring Absolute Value Functions and Transformations

Learn to use absolute value functions and their transformations, including graphing tips. Understand how to identify points on the graph, determine the opening direction based on the value of 'a', and apply translations horizontally and vertically. Discover how to graph step functions using multiple equations for different domain sections.

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Exploring Absolute Value Functions and Transformations

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  1. Algebra II 2.7: Use Absolute Value Functions and Transformations HW: p.127 (4-20 even)

  2. Absolute Value Function Graph

  3. Absolute Value Function Graph

  4. Graph

  5. Graph

  6. Graph

  7. Graph

  8. Graph

  9. What do you notice?

  10. What do you notice?

  11. How to Graph • Identify points on the graph • If a is positive the V will open up. • If a is negative the V will open down. • Translate the graph horizontally h units and vertically k units.

  12. Graph

  13. Graph

  14. Graph

  15. 2.7 Do Now: Graph

  16. Algebra II 2.7 extension: Use Piecewise Functions Quiz 1.3, 1.5, 2.7: Tomorrow

  17. What is a piecewise function? • At least two equations, each of which applies to a different part of the function’s domain.

  18. Evaluate the function g(x) above: • A.) x = 1 • B.) x = 5

  19. Graph

  20. Evaluate the function f(x) above: • A.) x = -4 • B.) x = -2 • C.) x = 0 • D.) x = 4

  21. Algebra II 2.7 extension: Use Piecewise Functions HW: p.131 (1-8 all)

  22. Graph

  23. Step function • A piecewise function is called a step function when it is defined by a constant value over each part of its domain. • Example:

  24. Graph

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