1. 4-3 Relations
Objective: Students will represent relations as sets of ordered pairs, tables, mappings, and graphs. Students will find the inverse of a relation.
S. Calahan
2008

2. Relation A set of ordered pairs. A relations can be represented as
In a table x y
3 4
Mapping x y Graph

3. Domain and Range
The domain is the set of the first numbers of the ordered pairs in a relation. (the x value)
The range is the set of the second number of the ordered pairs in a relations. (the y value)

4. Mapping Given the ordered pairs express the relation as a mapping.
A mapping illustrates how each element of the domain is paired with an element in the range.
Given the ordered pairs express the relation as a mapping.
(1, 2), (-2, 4), (0, -3), (1, 5)
x y
If a value is repeated in the range
or the domain only list it once in
the mapping. -3

5. Tables (1, 2), (-2, 4), (0, -3), (1, 5) x y 1 2 -2 4 0 -3 1 5
Express the relation as a table.
(1, 2), (-2, 4), (0, -3), (1, 5)
x y
In a table you write each value even if it is repeated.

6. Determine the domain and range
(1, 2), (-2, 4), (0, -3), (1, 5)
The domain for this relation is
{1, -2, 0}.
The range for this relation is
{2, 4, -3, 5}.
If a value is repeated list it only once.

7. Inverse Relations
The inverse of any relation is obtained by switching the coordinates in each ordered pair.
In a relation (a, b)
the inverse is (b, a)

8. Inverse Relation (1, 2), (-2, 4), (0, -3), (1, 5)
Express the inverse relation
(2, 1), (4, -2), (-3, 0), (5, 1)