This example is a relation but it is not a function because two students could each study for the same amount of time but earn two different grades.
mathematics
Description
This example is a relation but it is not a function because two students could each study for the same amount of time but earn two different grades. There are many ways to represent both relations and functions including mapping diagrams and points on the xy-plane. Mapping diagrams represent how the values in the input set relate to the values in the output set. Remember that the set of input values are called the domain, and the set of output values are the range. You can state the domain and range of any relation. When a relation is represented on the xy-plane, it can be shown with coordinate points, a line, or a curve. In these instances, the values on the horizontal axis (generally x-values), represent the domain and the values on the vertical axis (generally y-values), represent the range. You can use the domain and the range of a graph to determine if that graph represents a function. When two or more points on a graph are vertically aligned, then that graph represents a relation that is not a function. This is sometimes referred to as using the vertical line test. Use the information above to help you explore and answer questions related to functions, domain, and range.
