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Understanding Absolute Value Transformations in Graphing Functions

This resource explores the transformations of absolute value functions. It covers how to shift graphs vertically and horizontally based on parameters 'a' and 'b', as well as the effects of the constant 'c' on the graph's width. Practical examples are provided, illustrating how to graph these transformations step-by-step. Readers will enhance their understanding of function behavior through interactive graphing exercises aimed at enriching mathematical comprehension with technology.

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Understanding Absolute Value Transformations in Graphing Functions

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  1. Transformationsof Functions Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology

  2. Absolute ValueAn Absolute Value graph is always in a “V” shape.

  3. Given the following function, If: a > 0, then shift the graph “a” units up If: a < 0, then shift the graph “a” units down

  4. Given the following function, Since a > 0, then shift the graph “3” units up

  5. Let’s Graph

  6. How will the graph look?

  7. Let’s Graph

  8. How will the graph look?

  9. Let’s Graph

  10. How will the graph look?

  11. Let’s Graph

  12. Given the following function, We get the expression (x - b) and equal it to zero x - b = 0 x = b If: b> 0, then shift the graph “b” units to the rightIf: b< 0, then shift the graph “b” units to the left

  13. Given the following function, x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit right

  14. Let’s Graph

  15. How will the graph look?

  16. Let’s Graph

  17. How will the graph look?

  18. Let’s Graph

  19. How will the graph look?

  20. Let’s Graph

  21. Graphing Recall: Shift “3” units up since 3 > 0 then we use the expression x + 1, and equal it to zero x +1 = 0 x = -1 Since –1 < 0, then we shift “1” unit to the left

  22. Let’s Graph

  23. How will the graph look?

  24. Let’s Graph

  25. How will the graph look?

  26. Let’s Graph

  27. How will the graph look?

  28. Let’s Graph

  29. Given the following function, For this equation, c determines how wide or thin it will be. if: |c|>1, then the graph is closer to the y-axis if: |c|=1, then the graph remains the same if: 0<|c|<1, then the graph is further from the y-axis if c is a negative number, then the graph will reflect on the x-axis

  30. Given the following function, Since |5| > 0, then the graph is closer to the y-axis

  31. Let’s Graph

  32. How will the graph look?

  33. Let’s Graph

  34. How will the graph look?

  35. Let’s Graph

  36. How will the graph look?

  37. Let’s Graph

  38. How will the graph look?

  39. Let’s Graph

  40. Given the following function, Since 4 > 0, shift the graph “4” units up x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit to the right Since |5| > 0 shift the graph closer to the y-axis.

  41. Let’s Graph

  42. How will the graph look?

  43. Let’s Graph

  44. How will the graph look?

  45. Let’s Graph

  46. How will the graph look?

  47. Let’s Graph

  48. How will the graph look?

  49. Let’s Graph

  50. How will the graph look?

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