One of the basic definitions in calculus employs the ratio:
Source: MICDS
A discrete function or relation is one in which the domain can be represented by a finite number of values. For example, if we consider the relation , we see that the graph represents a set of individual points. This relation can further be classified as a discrete function as it also passes the vertical line test.
A continuous function or relation is one in which the domain contains an infinite number of points and the graph can be represented by a smooth curve or line. For example, consider the function . The domain consists of all real numbers x, and the graph is shown in the figure below.
Source: MICDS