4.1.2 Relations and Functions (continued) Example 2 Finding the Domain and Range of a Relation
In Example 2, Prof. Burger identifies the domain and range of a relation that is represented as a graph. The graph is a line segment with endpoints (3, 8) and (7, 2). Because the endpoints are solid circles, the endpoints are included in the relation. To find the relation’s domain, identify the least and greatest x -values, which are at the segment’s endpoints. Similarly, to find the relation’s range, identify the least and greatest y -values, which are also at the segment’s endpoints.
Example 3 Identifying Functions
In Example 3, Prof. Burger identifies the domain and range of relations that are represented as a table, mapping diagram, or a graph. Note that domain or range values that appear multiple times in a relation are listed only once in the set for the domain or range. For example, for the relation {(1, 2), (1, 3), (6, 5)}, the domain is {1, 6} and the range is {2, 3, 5}. So, even though the relation is a set of three ordered pairs, the domain contains only 2 values, because two of the ordered pairs have the same x -value. Prof. Burger also determines whether each relation is a function. A function is a special type of relation that pairs each of its domain values with exactly one range value. If a relation pairs a domain value with more than one range value, then that relation is not a function. For example, again consider the relation {(1, 2), (1, 3), (6, 5)}. The domain value 1 is paired with range values 2 and 3. Because the relation contains a domain value that is paired with two range values, it is not a function.
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