MTH 100
Relations and Functions
Objectives
1. Find the Domain and Range of a Relation.
2. Determine if Relations are Functions.
3. Determine if Graphs are Functions.
Objectives 1 and 2
• A relation is a set of ordered pairs.
• The domain of a relation is the set of first
coordinates.
• The range of a relation is the set of second
coordinates.
• A function is a relation in which no two
ordered pairs have the same first coordinate.
Objectives 1 and 2 Examples
• For each of the following relations:
1. Find the domain.
2. Find the range.
3. Tell whether the relation is a function.
{(3, -2), (6, 5), (3, 8), (-1, -10)}
{(-6, 5), (-1, 5), (4, 5), (9, 5), (14, 5)}
Objective 3
• The vertical line test is used to determine if a
given graph represents a relation or a
function.
• If it is possible to draw a vertical line that
intersects the graph in more than one point,
the graph does not represent a function.
Objective 3 Examples