Determine whether each relation defines a function. See Example 1. x y 3 -4 7 -4 10 -4

검증된 단계별 안내

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

Look at the given pairs: (3, -4), (7, -4), and (10, -4). Identify the x-values: 3, 7, and 10.

Check if any x-value repeats with a different y-value. Here, each x-value is unique and appears only once.

Since each x-value maps to exactly one y-value, the relation satisfies the definition of a function.

Conclude that the given relation defines a function because no x-value is associated with more than one y-value.

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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 (x-value) corresponds to exactly one output (y-value). This means no x-value can be paired with more than one y-value. Understanding this helps determine if a given set of ordered pairs represents a function.

Relation vs. Function

A relation is any set of ordered pairs, while a function is a special type of relation with a unique output for each input. Identifying whether a relation is a function involves checking for repeated x-values with different y-values.

Evaluating Ordered Pairs

To determine if a relation defines a function, examine each ordered pair's x-values. If any x-value repeats with a different y-value, the relation is not a function. In the given set, all x-values are distinct, indicating it is a function.