1. 1.6 - Relations

2. Relation

3. Relation – a set of ordered pairs

4. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)

5. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations:

6. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set

7. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table

8. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table
on a graph

9. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table
on a graph
in a mapping

10. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table
on a graph
in a mapping
Example 1
(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:

11. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table
on a graph
in a mapping
Example 1
(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:
1. a table

12. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table
on a graph
in a mapping
Example 1
(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:
1. a table x y

13. Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table
on a graph
in a mapping
Example 1
(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:
1. a table x y

14. -1 -3 -2 Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table
on a graph
in a mapping
Example 1
(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:
1. a table x y -1 -3 -2

15. -1 -3 -2 Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table
on a graph
in a mapping
Example 1
(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:
1. a table x y -1 -3 -2

16. -1 2 -3 -2 Relation – a set of ordered pairs
(relationship btw. 2 numbers!)
Ways to Represent Relations: as a set
in a table
on a graph
in a mapping
Example 1
(a) Express the relation {(-1,2),(0,-3),(-3,2),(-2,-2)} as:
1. a table x y -1 2 -3 -2

17. 2. a graph

18. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

19. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

20. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

21. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

22. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

23. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

24. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

25. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

26. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

27. 2. a graph
Graph the set of ordered pairs{(-1,2),(0,-3),(-3,2),(-2,-2)}

28. 3. a mapping

29. 3. a mapping
X Y

30. 3. a mapping
X Y -3 -2 -1

31. 3. a mapping
X Y

32. 3. a mapping
{(-1,2),(0,-3),(-3,2),(-2,-2)}
X Y

33. 3. a mapping
{(-1,2),(0,-3),(-3,2),(-2,-2)}
X Y

34. 3. a mapping
{(-1,2),(0,-3),(-3,2),(-2,-2)}
X Y

35. 3. a mapping
{(-1,2),(0,-3),(-3,2),(-2,-2)}
X Y

36. 3. a mapping
{(-1,2),(0,-3),(-3,2),(-2,-2)}
X Y

37. Inverse Relation

38. Inverse Relation - switch the x and y values in each ordered pair!

39. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation. x y 2 -4 3 5 -7 6 -8

40. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation. x y 2 -4 3 5 -7 6 -8

41. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation. x y 2 -4 3 5 -7 6 -8

42. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4), x y 2 -4 3 5 -7 6 -8

43. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4), x y 2 -4 3 5 -7 6 -8

44. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4), x y 2 -4 3 5 -7 6 -8

45. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4), x y 2 -4 3 5 -7 6 -8

46. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7), x y 2 -4 3 5 -7 6 -8

47. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7), x y 2 -4 3 5 -7 6 -8

48. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)} x y 2 -4 3 5 -7 6 -8

49. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)} x y 2 -4 3 5 -7 6 -8

50. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: x y 2 -4 3 5 -7 6 -8

51. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: x y 2 -4 3 5 -7 6 -8

52. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6} x y 2 -4 3 5 -7 6 -8

53. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: x y 2 -4 3 5 -7 6 -8

54. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: x y 2 -4 3 5 -7 6 -8

55. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: {-8, -7, -4} x y 2 -4 3 5 -7 6 -8

56. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: {-8, -7, -4} x y 2 -4 3 5 -7 6 -8

57. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: {-8, -7, -4} x y 2 -4 3 5 -7 6 -8

58. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: {-8, -7, -4} x y 2 -4 3 5 -7 6 -8

59. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: {-8, -7, -4}
Inverse: x y 2 -4 3 5 -7 6 -8

60. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: {-8, -7, -4}
Inverse: {(-4,2) x y 2 -4 3 5 -7 6 -8

61. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: {-8, -7, -4}
Inverse: {(-4,2),(-4,3) x y 2 -4 3 5 -7 6 -8

62. Inverse Relation - switch the x and y values in each ordered pair!
Example 2
Express the relation as a set of ordered pairs. State the domain and range, then write the inverse relation.
{(2,-4),(3,-4),(5,-7),(6,-8)}
Domain: {2, 3, 5, 6}
Range: {-8, -7, -4}
Inverse: {(-4,2),(-4,3),(-7,5)(-8,6)} x y 2 -4 3 5 -7 6 -8