Relationship that describes a phenomenon that varies constantly in sections. Therefore, it is a combination of relationship of zero variation and a relationship that characterizes the gaps (jumps between levels).

A step function is a function that is constant over the intervals of the independent variable and that changes abruptly for certain values of the independent variable. These values are called the

**critical values**of the function.A step function is a discontinuous function, since its graph cannot be drawn without lifting the pencil from the paper.

### Examples

- The
*floor*function defined by the relationship*f*(*x*) = [*x*] is an example of a step function in which the gaps (or levels) are intervals of the same length.

In this case, the relationship that characterizes the gaps is a relationship of direct variation. - The graph below represents a step function where the relationship that characterizes the gaps is a relationship of exponential variation.
- The mathematical model that best describes the number of passengers on a commuter train as a function of the time elapsed between the departure station and the arrival station is that of a step function.