In mathematics, functions describe relationships between two or more quantities. A step function is a special type of relationship in which one quantity increases in steps in relation to another quantity.

For example, postage cost increases as the weight of a letter or package increases. In the year 2001 a letter weighing between 0 and 1 ounce required a 34-cent stamp. When the weight of the letter increased above 1 ounce and up to 2 ounces, the postage amount increased to 55 cents, a step increase.

A graph of a step function f gives a visual picture to the term "step function." A step function exhibits a graph with steps similar to a ladder.

The domain of a step function f is divided or partitioned into a number of intervals. In each interval, a step function f(x) is constant. So within an interval, the value of the step function does not...