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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