Under what condition can a relation be classified as a function?

A relation can be classified as a function when each input value is associated with exactly one output value. This means that for every value in the domain (the set of input values), there is a unique value in the range (the set of output values).

This characteristic ensures that there is a consistent mapping from inputs to outputs, which is fundamental to defining a function. If there were an input that corresponded to multiple outputs, it would violate the definition of a function, making the relation non-function.

Conversely, the other options describe scenarios that do not meet the criteria for functions, such as having no outputs for an input or allowing multiple outputs for a single input. These situations disrupt the one-to-one correspondence required for a relation to be classified as a function.