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

Verified step by step guidance

1. Understand the definition of a function: A relation is a function if every input (x-value) corresponds to exactly one output (y-value).
2. Look at the given pairs: (3, -4), (7, -4), and (10, -4). Identify the x-values: 3, 7, and 10.
3. Check if any x-value repeats with a different y-value. Here, each x-value is unique and appears only once.
4. Since each x-value maps to exactly one y-value, the relation satisfies the definition of a function.
5. Conclude that the given relation defines a function because no x-value is associated with more than one y-value.

Key Concepts

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.