# How do you know whether a relation is a function and what the domain and range is for #(1,-3), (6,-2), (9,-1), (1,3)#?

##### 2 Answers

This relation is not a function.

The domain of this relation is

The range of this relation is

#### Explanation:

A relation is a function if no two ordered pair in the relation have the same first element and different second elements.

(That is; If two different pair have the same first element then the relation is **not** a function.)

In

the pairs

The domain if the set of all first elements.

So the domain of your relation is

The range is the set of second elements.

So the range of your relation is

**Note**

(Not all introductory level classes include domains and ranges for arbitrary relations. Some only mention domain and range for functions.)

The given points DO NOT represent a function.

Domain

Range

#### Explanation:

A relation is a function if, for EACH

As soon as there is a choice for

So

It does not matter than several

In the given ordered pairs, if

This is therefore NOT a function.

The Domain is the set of all the

The Range is the set of all the

For the given ordered pairs:

Domain

Range