A relation is a connection between the elements of a set or the elements of two sets.
e.g. "is greater than" and " is twice the size of " are examples of relations.
A function is a special type of relation.
Representation
Relations can be represented in several ways:
 As a set of ordered pairs.
e.g. A = {(1, 2), (2, 3), (3, 4)}
The first value in each ordered pair is the xvalue.
The second value in each ordered pair is the yvalue.
 As an arrow graph or mapping.
e.g. The domainThe range
The set of yvalues is called the range. i.e. {2, 3, 4}
 In table form
e.g.
 On a graph.
e.g.
 By a rule or formula.
e.g. y = x + 1
A function is a relation where each of the members of the domain,(each x value) is connected to only one member of the range, (the y value). Most relations are also functions.
Exceptions are relations such as x^{ 2} + y^{ 2} = 9 which has a graph of a circle. This relation is not a function.
Sequences
In mathematics, numbers are often arranged in a sequence. These sequences can be shown be a formula or function.
Often a sequence follows a rule or pattern.
Easy Sequence
Some sequences are obvious: 2, 4, 6, 8, 10...
This is the sequence of EVEN numbers.
The formula for this sequence is 2n where n stands for a counting number.
To find the next number in this sequence, calculate 2 × 6 = 12
Slightly Harder Sequence
The sequence 1, 4, 9, 16, 25... is the sequence of square numbers.
Comparing this sequence to the set of counting numbers {1, 2, 3, 4..}
1

2

3

4

5

...

1

4

9

16

25

...

The formula for this sequence is n^{2}^{.}
The next number in this sequence is 6^{2} = 36
More Difficult Sequence
The number of diagonals in polygons forms a sequence.
Name of polygon

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Number of sides 
3

4

5

6

7

Number of diagonals 
0

2

5

9

14

The sequence for the number of diagonals is 0, 2, 5, 9, 14...
The pattern for this sequence is an increase of 2, 3, 4 between each term.
The formula for this sequence is (n^{2} + n − 2)/2
The next number in this sequence is 20