# Math 10 Week 10: Relations versus Functions

What is a relation? What is a Function? What is the difference between the two?

A Relation is a number that is associated with many different numbers, for example, 2 = 3 and 2 = 4.

It’s best if you think of it like x and y so, 2,3 and 2,4

A Function is when a number is associated with one number, for example, 2,3 and 4,6

The difference between the two is that the x value will never have two different y values, though the same y value can have many different x values.

Think of relations like air, food and water. They are all things that you need, as you are the x value, and the air, food and water are the y values.

For example: lets say you are 1, and air is 2, food is 3, and water is 4. You would list them as 1,2 1,3 1,4

Think of functions like living. Everyone has a life, though you can only have 1 life. (unless reincarnation exists).

Lets say you are 1, person B is 2, person C is 3, and life is 4. You would list it as 1,4 2,4 3,4.

These are just many examples of relations and functions.

Relations must have 2 of the same x values to be a relation

Functions must have no repeating x values, but y values can be repeated.

So that’s it for Relations vs Functions, next week we will be talking about… either interpreting functions or distance between points, See ya next week!