Determine whether each relation defines a function.

Verified step by step guidance

1. 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).
2. Identify the set of input values (x-values) in the given relation.
3. Check if any input value is paired with more than one output value. If yes, then the relation is not a function.
4. If each input value has only one unique output value, then the relation defines a function.
5. Summarize your conclusion based on the above check: state clearly whether the relation is a function or not.

Key Concepts

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.