Determine whether each relation defines a function, and give the domain and range. {(2,5),(3,7),(3,9),(5,11)}

검증된 단계별 안내

Recall that a relation defines a function if every input (x-value) corresponds to exactly one output (y-value).

Examine the given relation: \(\{(2,5),(3,7),(3,9),(5,11)\}\). Notice that the input \(3\) is paired with two different outputs, \(7\) and \(9\).

Since the input \(3\) has more than one output, this relation does not define a function.

To find the domain, list all the unique input values: \(\{2, 3, 5\}\).

To find the range, list all the output values from the pairs: \(\{5, 7, 9, 11\}\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Definition of a Function

A function is a relation where each input (domain element) corresponds to exactly one output (range element). If any input is paired with more than one output, the relation is not a function. This concept helps determine if the given set of ordered pairs defines a function.

Domain of a Relation

The domain is the set of all first elements (inputs) from the ordered pairs in a relation. Identifying the domain involves listing all unique input values, which is essential for understanding the scope of the relation.

Range of a Relation

The range is the set of all second elements (outputs) from the ordered pairs in a relation. Determining the range involves listing all unique output values, which helps describe the possible results of the relation.