What is a relation?
A relation is a rule that connects the members of one set to the members of another. It is written as a set of ordered pairs (x, y). The set of first members is the domain and the set of second members that are actually used is the range. The set the pairs may be drawn from on the right is the codomain.
Worked exampleDomain and range
The relation R = {(1, 2), (2, 4), (3, 6), (4, 8)}. State the domain and the range.
- Domain: all the first members.
- Range: all the second members.
Answer: The rule is y = 2x. Domain {1, 2, 3, 4}, range {2, 4, 6, 8}.
Graph of a relation
A relation can be drawn as dots on a coordinate plane, one for each ordered pair, or as a curve when x can take any real value in an interval. Each relation can also be shown with an arrow diagram.
Types of relation
| Type | Meaning | Example |
|---|---|---|
| One-to-one | Each x has its own y | y = x + 1 |
| Many-to-one | Several x share the same y | y = x² |
| One-to-many | One x has several y | x = y² |
| Many-to-many | Several x and several y | is a factor of |
Try itDomain and range of y = 2x + 1
Choose the smallest and largest x. See the range of y.
Key terms
- Relation
- A rule linking members of one set to another.
- Domain
- The set of first members.
- Range
- The set of second members that are used.
- Ordered pair
- A pair (x, y) in which the order matters.
Summary
- A relation is a set of ordered pairs.
- The domain is the set of x values and the range is the set of y values.
- A graph shows each ordered pair as a point.
- Relations may be one-to-one, many-to-one, one-to-many or many-to-many.