Which method below does not define a function?

A method that fails to define a function primarily involves cases where the same output value can be associated with multiple input values. In this scenario, if different x-values (inputs) result in the same y-value (output), the relationship does not satisfy the definition of a function.

A function, by its very definition, requires that for each input there is exactly one output. This condition is maintained when each value on the x-axis maps to a unique value on the y-axis, which is not the case when there are repeating y-values for various x-values. Thus, the presence of non-unique outputs signals that the relationship does not fulfill the criteria for being categorized as a function.

Understanding this differentiation is crucial when analyzing various types of relationships in mathematics since it lays the foundation for more complex functions and graph interpretations.