Year 10 Interactive Maths - Second Edition

## Relations

In mathematics, we use symbols to denote relations and we build mathematical sentences using numbers, pronumerals and relations.

###### Consider the following sentence:

The cost (in dollars) of buying pens is equal to ten times the number of pens bought.

If c represents the cost in dollars and p represents the number of pens bought, then this sentence can be expressed mathematically as

###### This suggests the following definition:

A relation is a set of ordered pairs, and is usually defined by a rule.

### Domain

The domain of a relation is the set of all first elements (usually x values) of its ordered pairs.

### Range

The range of a relation is the set of all second elements (usually y values) of its ordered pairs.

###### Note:

The graph of c against p is discrete because p is an element of the set of natural numbers. The values of c depend upon p. So, we say that p is an independent variable and c is a dependent variable.

#### Example 1

State the domain and range of the following relations:

## Functions

A relation is said to be a function if each element of the domain determines exactly one element of the range.

### Domain of a Function

The domain of a function is the set of all first elements (usually x values) of its ordered pairs.

### Range of a Function

The range of a function is the set of all second elements (usually y values) of its ordered pairs.

#### Example 2

State the domain and range of the following functions: