United States of America

Grade 8

We have explored relations and functions as ways of linking two sets of data, usually written using x's and y's as coordinates.

We'll now consider all the possible values of inputs and outputs that these relationships can have.

Domain and range both describe the span of values that a relation can take. Their definitions are very similar, but the small difference is very important.

We can find the domain and range of a relation no matter how it is represented. We simply need to look at the ordered pairs, graph, table, or other representation and list out all of the possible x and y-values that the relation can have, putting commas in between each value and curly braces on the outside. Do not repeat any values that show up more than once.

Typically the domain and range are written in ascending order (least to greatest) but that is not a requirement.

Consider the relation \{(1, 2), (5, 3), (2, 7), (5, -1)\}. State the domain and range.

Worked Solution

Consider the relation in the table.

x | 1 | 6 | 3 | 8 | 2 |
---|---|---|---|---|---|

y | 3 | 2 | 7 | 1 | 2 |

a

What is the domain of the relation?

Worked Solution

b

What is the range of the relation?

Worked Solution

c

Is this relation a function?

Worked Solution

Consider the relation on the graph below.

a

What is the domain of the relation?

Worked Solution

b

What is the range of the relation?

Worked Solution

c

Is this relation a function?

Worked Solution

Idea summary

**Domain** - all of the possible x-values of a relation

**Range** - all of the possible y-values of a relation