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Absolute Value Functions and Graphs

Absolute Value Functions and Graphs. Lesson 2-5. Important Terms.

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Absolute Value Functions and Graphs

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  1. Absolute Value Functions and Graphs Lesson 2-5

  2. Important Terms • Parent function: the simplest function with these characteristics. The equations of the function in a family resemble each other, and so do the graphs. Offspring of parent functions include translations, stretches, and shrinks. • Translation: it shifts a graph horizontally, vertically, or both. It results in a graph of the same shape and size but possibly in a different position • Stretch: a vertical stretch multiplies all y-values by the same factor greater than 1, thereby stretching the graph vertically • Shrink: a vertical shrink reduces y-values by a factor between 0 and 1, thereby compressing the graph vertically • Reflection: in the x-axis changes y-values to their opposites. When you change the y-value of a graph to their opposites, the graph reflects across the x-axis (creates a mirror image)

  3. The Family of Absolute Value Functions

  4. Families of Functions: Absolute Value Functions

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

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

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

  8. Let’s Graph

  9. How will the graph look?

  10. Let’s Graph

  11. How will the graph look?

  12. Let’s Graph

  13. How will the graph look?

  14. Let’s Graph

  15. 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

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

  17. Let’s Graph

  18. How will the graph look?

  19. Let’s Graph

  20. How will the graph look?

  21. Let’s Graph

  22. How will the graph look?

  23. Let’s Graph

  24. 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

  25. Let’s Graph

  26. How will the graph look?

  27. Let’s Graph

  28. How will the graph look?

  29. Let’s Graph

  30. How will the graph look?

  31. Let’s Graph

  32. 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

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

  34. Let’s Graph

  35. How will the graph look?

  36. Let’s Graph

  37. How will the graph look?

  38. Let’s Graph

  39. How will the graph look?

  40. Let’s Graph

  41. How will the graph look?

  42. Let’s Graph

  43. 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.

  44. Let’s Graph

  45. How will the graph look?

  46. Let’s Graph

  47. How will the graph look?

  48. Let’s Graph

  49. How will the graph look?

  50. Let’s Graph

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