FunctionsA special type of relation!

Image from MathisFun.com

Let’s review relations!

• A relation is a set of ordered pairs. {(1,2), (2,-3), (-2,4), (-1,0)} is an example of a relation.

• The x-values in each coordinate make up what is referred to as the domain. {-2, -1, 1, 2} is the domain of the relation.

• The y-values in each coordinate make up what is referred to as the range. {-3, 0, 2, 4} is the range of the relation.

So What Are Functions?

• Functions are relations, so they are sets of ordered pairs!

• What makes them special is that the x-values don’t repeat!

• Each x-value is paired with exactly one y-value.

• There are many ways to express functions.

• They can be expressed as ordered pairs, in tables, in a graph, or as a mapping.

Let’s take a closer look at how functions can be expressed.

• Let’s use the relation:{(-2,3), (1, 4), (0, 4), (-1, 2)}.

This relation is a function because the x-values don’t repeat.

It is expressed here as a set of ordered pairs.

We can also use a table to express this function.

x y

-2 3

-1 2

0 4

1 4

A Mapping is another way to express functions.

You can express a function as a mapping. A mapping is two ovals. The first oval contains the domain (x-values). The second oval contains the range (y-values).

For example: This is an example of a mapping. Each

x-value is mapped or paired with exactly

one y-value.

-1 0 1 2

-2 1 2

You can also express functions in a graph.

Here are some examples of functions in graphs:

Images from OCS Algebra IA U4L3 Guided Notes

Graphs of Functions

You can tell if the graph of a relation is a function if it passes something called

the Vertical Line Test. The VLT says that if you draw a vertical line through a graph and it intersects the graph in exactly one point, then the graph is a function.

This is the graph of a function; it passes the VLT.

This is not the graph of a function; it fails the VLT.

Images from OCS Algebra IA Unit 4 Lesson 3