Which statement correctly characterizes a non-function?

A non-function is characterized by the fact that a single input (x-value) can be associated with multiple outputs (y-values). Therefore, the option stating that two ordered pairs share the same x-coordinate is correct, as it exemplifies a situation where a non-function occurs. In a non-function, when the same x-coordinate corresponds to different y-values, it violates the definition of a function, which requires that each input must map to one and only one output.

The other options reflect properties of functions. For example, stating that each x-value must correspond to exactly one y-value defines the fundamental characteristic of a function. Similarly, the idea that all ordered pairs are unique pertains to the uniqueness of each pair in a function's graph, not to its non-functional characteristic. Lastly, the statement about every output being represented by a unique input directly aligns with a function's definition, highlighting the contrast between a function and a non-function.