You can use the vertical line test on a graph to determine whether a relation is a function. If it is impossible to draw a vertical line that intersects the graph more than once, then each x-value is paired with exactly one y-value. So, the relation is a function. If it is possible to draw a vertical line that intersects the graph more than once, then there is an x-value that is paired with more than one y-value. So, the relation is not a function.

A relation is a function if each x-value is paired with exactly one y-value.

A function is a special type of relation in which each element of the domain is paired with exactly one element in the range. A mapping shows how the elements are paired. Its like a flow chart for a function, showing the input and output values.A mapping diagram consists of two parallel columns. The first column represents the domain of a function f , and the other column for its range. Lines or arrows are drawn from domain to range, to represent the relation between any two elements. A function represented by the mapping in the first diagram, in which each element of the range is paired with exactly one element of the domain, is called one-to-one mapping. In the second diagram, the first element in the domain has mapped with more than one element in the range. If one element in the domain mapped with more then one element in the range, the mapping is called one-to-many relation. One-to-many relations are not functions.

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value. A function is written as f x , where x is the input value. The general form of a function is y = f x.