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Functions and Relations
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Functions

Example 2

Determine whether each relation is a function.

a. {(3,8),(5,2),(7,2),(9,7)}
b. {(2,5),(3,7),(4,9),(3,11)}


Solution

a. As shown in the figure below, no two different ordered pairs in the given relation have the same first coordinate. Every element in the domain corresponds to exactly one element in the range. Thus, the given relation is a function.

b. Two ordered pairs have the same first coordinate and different second coordinates. The diagram below shows that the first coordinate 3 is paired with 7 and 11. Thus, the relation is not a function.