1. Relations and Functions Objective: To use tables and graphs to represent relations and functions.

2. Relations and Functions A Relation is a set of ordered pairs. The set of the first coordinates (x) is called the domain of the relation. The set of the second coordinates (y) is called the range of the relation.

3. Relations and Functions Example: xy -45 -26 02 Domain: {-4, -2, 0} Range: {5, 6, 2}

4. Relations and Functions A Function is a relation in which each element of the domain is paired with exactly one element in the range.

5. Relations and Functions Example: xy -45 -26 02 17 3-5

6. Relations and Functions Example: xy -45 -26 02 17 3-5

7. Relations and Functions Example: xy -45 -26 02 17 3-5

8. Relations and Functions Example: xy -45 -26 02 17 3-5

9. Relations and Functions Example: xy -45 -26 02 17 3-5

10. Relations and Functions Example: xy -45 -26 02 17 3-5

11. Relations and Functions Example: xy -45 -26 02 17 3-5

12. Relations and Functions Example: xy -45 -26 02 17 3-5 The vertical line test can be used to determine if the relation is a function. Use a straight edge moved slowly across the graph to see if two point touch the edge at the same time. This is a true test for all functions.

13. Relations and Functions Example: xy Your turn to make a function.

14. A mapping shows how each member of the domain is paired with each member in the range. Functions Domain Range -3 0 2 124124 one-to-one function Relations and Functions

15. This mapping is not a one to one relationship. It is still a function. Different x –values can produce the same y- value. Functions Domain Range 1 4 5353 function, not one-to-one Relations and Functions

16. This mapping is NOT a Function! Can you tell why? Functions Domain Range 5 -3 1 601601 not a function Relations and Functions

17. How do we know if the relation is a function? Mapping: Every x matches to only one y-value Ordered Pairs: Any x value has only one corresponding y- value Graph: Use the vertical line test Table: Each x value matches only one y value -2 3 4 6 3 8 12 xy {(0, 2), (-3, 1), (4, -5), (7, 4)}

18. Relations and Functions Assignment: