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.
- 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.