What is a correct definition of a function?

A function is defined as a relation in which each input corresponds to exactly one output. This means that for any given value of the independent variable (often represented as x), there is a unique value of the dependent variable (often represented as y). This definition ensures that no input can produce more than one output, making functions predictable and well-defined.

For example, if you consider the function f(x) = x^2, for each input value of x (such as 2), there's a single output value (which would be 4). This relationship sustains the essence of what a function is, allowing for consistent evaluation.

The other options do not align with this fundamental definition. A relation with multiple outputs for each input would violate the single-output requirement, while a set of ordered pairs with the same x-values does not necessarily mean a function because some pairs could provide different outputs. Lastly, a mathematical expression representing a variable is too broad and does not specifically characterize the relationship between inputs and outputs fundamental to functions.