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High School Mathematics - 2
Functions, Relations, Domain & Range

Relation: A relation is simply a set of ordered pairs.

The first elements in the ordered pairs, the x-values, form the domain. The second elements in the ordered pairs, the y-values, form the range.

This mapping shows a relation from set A into set B. The relation consists of the ordered pairs (1,2), (1,3), (4,6), (5,6), and (7,8).
The domain is the set {1, 4, 5, 7}
The range is the set {2, 3, 6, 8}.
The range is the dependent variable.

A function is a set of ordered pairs in which each element of the domain has only ONE element associated with it in the range.

The relation shown above is NOT a function because the element 1 (in the domain) is mapped to two elements in the range, 2 and 3.

A function may have two x-values assigned to the same y-value, but may not have two y-values assigned to the same x-value.


Domain = {1,4,5,7}
Range = {2,3,6,8}
Relation = {(1,2), (4,3), (5,6), (7,8)}
This relation is a function.

Directions: Answer the following. Enclose the answer in curly brackets { }. Also write at least 5 examples of your own.