Determine whether each relation defines a function.

Verified step by step guidance

1. Understand the definition of a function: A relation defines a function if every input (or domain element) corresponds to exactly one output (or range element).
2. Identify the inputs and outputs in the given relation. The inputs are the first elements of each ordered pair, and the outputs are the second elements.
3. Check if any input value is paired with more than one output value. If an input repeats with different outputs, the relation is not a function.
4. If every input has only one unique output, then the relation defines a function.
5. Summarize your conclusion based on the above check: state whether the relation is a function or not, providing reasoning based on the input-output pairs.

Key Concepts

Relation

A relation is a set of ordered pairs where each input (or domain element) is associated with one or more outputs (or 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.