In mathematics, a relation is not considered a function if it fails to meet a specific criterion known as the vertical line test. This test states that if you can draw a vertical line through a graph of the relation and it intersects the graph at more than one point, then the relation is not a function.
For example, consider the relation that pairs each x-coordinate with multiple y-coordinates. If you have a set of points where for a single x-value there are multiple corresponding y-values, this means that the x-value is associated with more than one output, violating the definition of a function.
Another way to think about it is through the definition of functions. A function, by definition, assigns exactly one output (y) for each input (x). Any instance where there is ambiguity or multiple outputs for a single input indicates that the relation in question is not a function. Therefore, characteristics such as repeating x-values with different y-values are definitive indicators that a relation is not functioning as a proper function.