2. A relation is an operation, or series of operations, that maps one number onto another.

3. You can think of a relation as a machine that uses numbers to produce other numbers.

4. This machine adds 5 to any number you put into it.

5. What relation does this machine represent?

6. One possibility is that each number is multiplied by –2.

7. What relation does this machine represent?

8. One possibility is that each number is divided by 2.

9. In this relation, -5 is mapped onto 12, 1 is mapped onto 18, and 100 is mapped onto 117.

10. The relation would map 3 onto which number?

11. If you see the relation as adding 17 to each number, you could say that 3 maps onto 20.

12. What number maps onto 0?

14. Find the missing numbers:

16. There is a name for the numbers that go into a relation.

17. Since we put them into the relation, it makes sense to call them input values.

18. And there is a name for the numbers that come out of a relation.

19. Since they come out of the relation, it makes sense to call them output values.

20. Find the output values if the input values are {1, 3, 5, 7}. InputOutput

21. Find the output values if the input values are {1, 3, 5, 7}. InputOutput

22. Find the output values if the input values are {1, 3, 5, 7}. InputOutput

23. Find the output values if the input values are {1, 3, 5, 7}. InputOutput

24. Relation - Any set of ordered pairs {(1,6), (2,7), (3,8), (4,9)} Function - A special type of relation where there is exactly one output for every input. For every x, there is exactly one y. xy 1 2 6 7 xy 1 2 6 7 Not a Function Function

25. yx -2 0 1 2 -4 -2 0 2 4 y = 2x input output -2 -4 -2 0 1 0 2 24 x-y Chart or Table Mapping Diagram Function

26. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function

27. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function

28. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Not a Function

29. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Not a Function

30. Vertical Line Test - Functions x y x y x y x y x y x y x y x y Function Not a Function Not a Function Not a Function Not a Function

31. Tell whether the relation below is a function. 1) 2) 3) 4) input output 0 1 5 2 3 yx -3 0 1 2 x y Function Not a Function Not a Function input output -2 0 3 4 5 6 Not a Function