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2.1 – Relations & Functions

2.1 – Relations & Functions. 2.1 – Relations & Functions. Relation. 2.1 – Relations & Functions. Relation – a set of ordered pairs. 2.1 – Relations & Functions. Relation – a set of ordered pairs (a relationship between numbers). 2.1 – Relations & Functions.

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2.1 – Relations & Functions

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  1. 2.1 – Relations & Functions

  2. 2.1 – Relations & Functions Relation

  3. 2.1 – Relations & Functions Relation – a set of ordered pairs

  4. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers)

  5. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs

  6. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y)

  7. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain

  8. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range

  9. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range Function

  10. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range Function – relation where each x has only one y value

  11. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range Function – relation where each x has only oney value

  12. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range Function – relation where each x has only oney value Note:

  13. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range Function – relation where each x has only oney value Note: each y can have more than one x value!

  14. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range Function – relation where each x has only oney value Note: each y can have more than onex value!

  15. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range Function – relation where each x has only oney value Note: each y can have more than one x value! *If each y does have only one x value, it is called a one-to-one function.

  16. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range Function – relation where each x has only oney value Note: each y can have more than one x value! *If each ydoes have only one x value, it is called a one-to-one function.

  17. 2.1 – Relations & Functions Relation – a set of ordered pairs (a relationship between numbers) ordered pairs – (x, y) domain range Function – relation where each x has only oney value Note: each y can have more than one x value! *If each ydoes have only one x value, it is called a one-to-one function.

  18. Example 1

  19. Example 1 {(-3,1),(0,2),(2,4)}

  20. Example 1 {(-3,1),(0,2),(2,4)} Domain Range

  21. Example 1 {(-3,1),(0,2),(2,4)} Domain Range

  22. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3

  23. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3

  24. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 0

  25. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 0

  26. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 0 2

  27. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 0 2

  28. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2

  29. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2

  30. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2

  31. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2

  32. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2 4

  33. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2 4

  34. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2 4

  35. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2 4

  36. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2 4 {(-1,5),(1,3),(4,5)} {(5,6),(-3,0),(1,1),(-3,6)}

  37. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2 4 {(-1,5),(1,3),(4,5)} {(5,6),(-3,0),(1,1),(-3,6)} Domain Range Domain Range

  38. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2 4 {(-1,5),(1,3),(4,5)} {(5,6),(-3,0),(1,1),(-3,6)} Domain Range Domain Range -1 -3 0 1 3 1 1 4 5 5 6

  39. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 0 2 2 4 {(-1,5),(1,3),(4,5)} {(5,6),(-3,0),(1,1),(-3,6)} Domain Range Domain Range -1 -3 0 1 3 1 1 4 5 5 6

  40. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 FUNCTION 0 2 1-1 2 4 {(-1,5),(1,3),(4,5)} {(5,6),(-3,0),(1,1),(-3,6)} Domain Range Domain Range -1 -3 0 1 3 1 1 4 5 5 6

  41. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 FUNCTION 0 2 1-1 2 4 {(-1,5),(1,3),(4,5)} {(5,6),(-3,0),(1,1),(-3,6)} Domain Range Domain Range -1 -3 0 1 3 1 1 4 5 5 6 FUNCTION

  42. Example 1 {(-3,1),(0,2),(2,4)} Domain Range -3 1 FUNCTION 0 2 1-1 2 4 {(-1,5),(1,3),(4,5)} {(5,6),(-3,0),(1,1),(-3,6)} Domain Range Domain Range -1 -3 0 1 3 1 1 4 5 5 6 FUNCTION Not a Function

  43. Example 2 Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (a) {(-2,1),(-1,-1,),(0,1),(-1,1)}

  44. Example 2 Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (a) {(-2,1),(-1,-1,),(0,1),(-1,1)}

  45. Example 2 Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (a) {(-2,1),(-1,-1,),(0,1),(-1,1)}

  46. Example 2 Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (a) {(-2,1),(-1,-1,),(0,1),(-1,1)}

  47. Example 2 Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (a) {(-2,1),(-1,-1),(0,1),(-1,1)}

  48. Example 2 Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (a) {(-2,1),(-1,-1),(0,1),(-1,1)}

  49. Example 2 Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (a) {(-2,1),(-1,-1),(0,1),(-1,1)}

  50. Example 2 Graph each relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (a) {(-2,1),(-1,-1),(0,1),(-1,1)}

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