Determine whether each relation is a function. Give the domain and range for each relation.{(1, 2), (3, 4), (5, 5)}

검증된 단계별 안내

Step 1: Recall the definition of a function. A relation is a function if every input (x-value) is associated with exactly one output (y-value).

Step 2: Examine the given relation {(1, 2), (3, 4), (5, 5)}. Check if any x-value is repeated with different y-values. If no x-value is repeated, the relation is a function.

Step 3: Identify the domain of the relation. The domain is the set of all x-values in the relation. For this relation, the x-values are {1, 3, 5}.

Step 4: Identify the range of the relation. The range is the set of all y-values in the relation. For this relation, the y-values are {2, 4, 5}.

Step 5: Conclude whether the relation is a function based on the analysis in Step 2. If no x-value is repeated, the relation is a function. Provide the domain and range as part of the final answer.

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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 specific type of relation where each input (or domain element) is associated with exactly one output (or range element). This means that no two ordered pairs can have the same first element with different second elements. Understanding this definition is crucial for determining if a given relation qualifies as a function.

Domain and Range

The domain of a relation is the set of all possible input values (first elements of the ordered pairs), while the range is the set of all possible output values (second elements). Identifying the domain and range helps in understanding the behavior of the function and its limitations. For the given relation, the domain and range can be easily extracted from the ordered pairs.

Ordered Pairs

Ordered pairs are pairs of elements written in the form (x, y), where 'x' is the input and 'y' is the output. In the context of relations and functions, the order of the elements is significant, as it determines the relationship between the input and output. Analyzing the ordered pairs in the relation allows us to assess whether it meets the criteria of a function.