1 / 31

Absolute Value Functions

Graphs and Compound Functions. Absolute Value Functions. Select the desired MENU option below Graphs 1. Translations Quick Graphs Graphing Inequalities Writing as Compound Functions 4. Using the vertex and slopes 5. From Definition. Absolute Value Functions. Translations.

damisi
Download Presentation

Absolute Value Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Graphs and Compound Functions Absolute Value Functions

  2. Select the desired MENU option below • Graphs • 1. Translations • Quick Graphs • Graphing Inequalities • Writing as Compound Functions • 4. Using the vertex and slopes • 5. From Definition Absolute Value Functions

  3. Translations Absolute Value Functions

  4. y =|x|

  5. y = |x+1| + 2 x+1 = 0 x = -1 2 1

  6. y = |2x+5| - 4 2x+5 = 0 x = -(5/2) 4 5/2 squeeze squeeze Slope: -2 Slope: 2

  7. stretch stretch y = 2 |x - 3| + 1 x - 3 = 0 x = 3 1 3 Slope: 2 Slope: -2

  8. stretch stretch y = 3 |2x - 3| - 4 2x - 3 = 0 x = 3/2 4 3/2 squeeze squeeze squeeze Slope: -3(2) = -6 Slope: 3(2) = 6

  9. Quick Graphs Absolute Value Functions

  10. y =|x|

  11. y = |x+1| + 2 x+1 = 0 x = -1 2 1

  12. y = |2x+5| - 4 2x+5 = 0 x = -(5/2) 4 5/2 squeeze squeeze Slope: -2 Slope: 2

  13. stretch stretch y = 2 |x - 3| + 1 x - 3 = 0 x = 3 1 3 Slope: 2 Slope: -2

  14. stretch stretch y = 3 |2x - 3| - 4 2x - 3 = 0 x = 3/2 4 3/2 squeeze squeeze squeeze Slope: -3(2) = -6 Slope: 3(2) = 6

  15. Graphing Inequalities Absolute Value Functions

  16. y ≤ |2x+5| - 4 2x+5 = 0 x = -(5/2) 4 Where do we shade? 5/2 squeeze squeeze Slope: -2 Slope: 2

  17. stretch stretch y > -2 |x - 3| + 1 x - 3 = 0 x = 3 Where do we shade? 1 3 Slope: 2 Slope: -2

  18. y ≥ |x+1| + 2 x+1 = 0 x = -1 Where do we shade? 2 1

  19. stretch stretch squeeze squeeze y < -2 |3x + 4| + 1 3x + 4 = 0 x = -4/3 Where do we shade? 1 4/3 Slope: (2)(3) = 6 Slope: -(2)(3) = -6

  20. stretch stretch squeeze squeeze y ≥3|-2x + 8| - 1 -2x + 8 = 0 x = 4 1 Where do we shade? 4 squeeze Slope: -3(2) = -6 Slope: 3(2) = 6

  21. Writing as Compound Functions using Vertex and slopes Absolute Value Functions

  22. y = | x + 2 | Slopes of sides m = ± 1 Vertex (-2, 0) left side right side What is missing? Compound function Jeff Bivin -- LZHS

  23. y = 3| x - 4 | Slopes of sides m = ± 3 Vertex (4, 0) left side right side What is missing? Compound function

  24. y = -2| x + 1 | Slopes of sides m = ± 2 Vertex left side right side Don't forget Compound function

  25. y = 2| x - 5 | +3 Slopes of sides m = ± 2 Vertex (5, 3) left side right side Don't forget Compound function

  26. y = -4| 2x - 5 | + 7 Slopes of sides m = ± 8 Vertex left side right side Don't forget Compound function

  27. Writing as Compound Functions From Definition Absolute Value Functions

  28. y = | x + 2 | If x > -2 If x < -2

  29. y = 3| x - 4 | If x > 4 If x < 4

  30. y = -2| x + 1 | If x > -1 If x < -1

  31. y = -3| 2x + 3 | + 1

More Related