What indicates that a relation is not a function?

A relation is not a function if it fails the Vertical Line Test. The Vertical Line Test is a visual way to determine if a graph represents a function. According to this test, if a vertical line drawn through a graph crosses it at more than one point, then the relation is not a function. This is because, for a relation to qualify as a function, each input (x-value) must correspond to exactly one output (y-value). If a single input can produce multiple outputs, it violates the fundamental definition of a function.

The other statements do not accurately reflect the characteristics of a function. For instance, a relation containing only one variable may or may not be a function; it depends on how the variable relates to other elements. Expressing something in function notation does not exclude it from being a function; in fact, it typically indicates that it is a function. Lastly, being defined in point-slope form does not determine whether a relation is a function, as many linear equations in that form are indeed functions. Thus, the Vertical Line Test is the definitive method for assessing whether a relation can be classified as a function or not.