Determine whether each relation defines a function.

검증된 단계별 안내

Recall the definition of a function: a relation is a function if every input (or x-value) corresponds to exactly one output (or y-value).

Identify the set of input values (x-values) in the given relation.

Check if any input value is paired with more than one output value. If yes, then the relation is not a function.

If each input value has only one unique output value, then the relation defines a function.

Summarize your conclusion based on the above check: state clearly whether the relation is a function or not.

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영상 길이:

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주요 개념

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

Relation

A relation is a set of ordered pairs where each input (domain element) is associated with one or more outputs (range elements). Understanding what constitutes a relation is fundamental to analyzing whether it can be considered a function.

Function Definition

A function is a special type of relation where each input corresponds to exactly one output. This means no input value can be paired with more than one output value, ensuring a unique mapping from domain to range.

Vertical Line Test

The vertical line test is a graphical method to determine if a relation is a function. If any vertical line intersects the graph of the relation more than once, the relation is not a function because an input has multiple outputs.