Final answer:
For a relation to be considered a function, each input in the relation must have a unique output.
Step-by-step explanation:
For a relation to be considered a function, one key requirement is that each input (or x-value) in the relation must have a unique output (or y-value). This means that for any given input, there cannot be multiple outputs. If there are multiple outputs for the same input, the relation is not a function.
For example, let's consider the relation {(1, 2), (1, 3), (2, 4), (3, 5)}. In this relation, the input 1 has two different outputs, 2 and 3. Therefore, this relation is not a function.
On the other hand, if we have the relation {(1, 2), (2, 4), (3, 5)}, each input has a unique output, making it a function.