What is the difference between a function and a relation?

The distinction between a function and a relation is fundamentally about how inputs are paired with outputs. A function is a specific type of relation that adheres to a particular rule: for each input, there is exactly one output. This means that no input can be associated with more than one output, which ensures a consistent mapping from inputs to outputs.

On the other hand, a relation is a broader concept that includes any set of input-output pairs. A relation can assign multiple outputs to a single input, which is not permissible in a function. For instance, if an input value corresponds to more than one output in a relation, it breaks the criteria required for that relation to be classified as a function. This is the key characteristic that sets functions apart from general relations.

Choosing the correct response emphasizes this fundamental property, showcasing how functions impose a stricter rule regarding the pairing of inputs and outputs, while relations can operate under more flexible associations.