1. Relations

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

3. For example, adding 3 is a relation.
We could write it as the relation,
It maps 5 onto 8, because 5+3 is 8.

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

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

6. What relation does this machine represent?

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

8. What relation does this machine represent?

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

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

11. The relation would map 3 onto which number?

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

13. What number maps onto 0?

14. What number maps onto 0?

15. Find the missing numbers:

16. Find the missing numbers:

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

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

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

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

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

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

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

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