Which of the following accurately describes a characteristic of a function?

A function is defined by a specific rule that relates each input to a single output. This fundamental characteristic ensures that for every value in the domain (input), there is a corresponding unique value in the range (output). Therefore, when considering the nature of functions, it is correct to say that every input must have exactly one output. This criterion guarantees the well-defined relationship that is essential for the operation of functions in mathematics.

In contrast, the other statements do not align with the definition of a function. For instance, claiming that every input must have multiple outputs directly contradicts the unique output requirement. Similarly, stating that each output can be linked to multiple inputs describes many-to-one relationships, which are permissible in functions but do not define their core characteristic. Lastly, the idea that an output can exist without an input implies a lack of dependence, which is not permissible in the context of a function since every output is tied to an input in a defined manner. This reinforces the importance of the specific relationship that defines a function, hence confirming that the correct characterization is that every input must have exactly one output.