1. Identifying and describing relations and functions
A relation is a set of ordered pairs. The following is an example of a
relation:
The domain of a
relation S is the set
S = {(1, 1), (1, 2), (3, 4), (5, 6)}
of all first elements
of the ordered pairs
The range of a
relation S is the set
of all second
elements of the
ordered pairs
A relation may be defined by a rule which pairs the elements in its
domain and range. Thus the set:
Gives the relation →

2. When the domain of a relation is not explicitly stated,
it is understood to consist of all real numbers for which the defining rule has
meaning.
Example 1.

3. (c) {(-2,-1), (-1,-1), (-1,1), (0,1), (1,-1)}

4. Sometimes the set notation is not used in the specification of a relation.
For the above example:
Functions are relations that are one-to-one or many-to-one

5. Fully defining functions
1. define the domain, and
2. state the rule.
In using this notation the
co-domain is not
necessarily the range.
It is a set that contains
the range.
There are numerous ways of describing the
same function, for eg.

6. Restriction of a function
We can create several different functions by defining different domains. For
example:
Example 3.

7. By calculator
Exercise 1B 1-5 ESO, 6-15 ESO