Which statement best describes a function?

A function is defined as a specific type of relation where each input is associated with exactly one output. This means that for any given input value, there can't be more than one corresponding output value; otherwise, it would not meet the criteria of being a function. This concept is fundamental in mathematics, particularly in algebra and calculus, as it provides a clear way to understand how outputs are determined by inputs.

The other statements do not accurately reflect the definition of a function. For instance, a relation with multiple outputs for a single input directly contradicts the definition of a function. An arbitrary collection of ordered pairs may or may not satisfy the condition of having a single output for each input, thus making it insufficient to define a function. Lastly, a random mathematical expression does not necessarily imply any specific relationship between inputs and outputs, and therefore does not adequately describe a function. The precision of the definition in the correct choice ensures clarity in mathematical communication.