FUNCTION RULES

Relations

A relation is a set of ordered pairs.

Let's take a look at a couple of examples:

A relation can be written in the form of a table.

A relation can also be written as a set of ordered pairs.

Think of a vending machine. You put in 75 cents and out pops your bag of chips. Or you put in a dollar and out pops your Hershey Bar.

There is a relationship between the amount of money that you put in the machine and what comes out!

Domain and Range

Domain: The set of input values.• The money you put into the vending machine.

Range: The set of output values.• The snack you get out!

Example 1: State the domain and range.

{(2,4) (3,6) (4,8) (5, 10)}

* Remember: Domain is the input and range is the output!

The domain contains the independent variable and the range contains the dependent variable. This means that the value of the range depends on the domain.

Think about the vending machine: What comes out of the machine (range) depends on what you put in (domain). You can't put in a nickel and expect a chocolate bar to pop out!

Functions!

Functions are a special type of relation.

In a function, each input (x coordinate) may be paired with only ONE output (y coordinate).

Let’s look at our relation from before:

b:{(2,4) (3,6) (4,8) (5, 10)}

How can we tell if it’s a function?

There are actually two ways to determine if a relation is a function.

1. One way is to analyze the ordered pairs2. The other way is to use the vertical line test.

Example 2Let's analyze our ordered pairs first.

Since each input has a different output, this can be classified as a function.

Let's verify it with the vertical line test. Drag your pencil across the graph. If it touches two points at the same time, it’s not a function!

b:{(2,4) (3,6) (4,8) (5, 10)}

Example 3: Is this a function?

{(-3, 2) (-1, 6) (1,2)}

Example 4: Is this a function?

{(3,3) (-1,0) (3,-3)}