Table of Contents

## Introduction to Step Function

A Step function is a mathematical function that takes a finite number of discrete steps, rather than a continuous range of values. It is represented by a graph that has a series of horizontal lines, rather than a smooth curve. Step functions are used to model situations where there is a sudden change in the input, such as when a light is turned on or off.

## Basic Definition of the Step Function

The step function is a mathematical function that has a discontinuity at a specific point in its domain. This function is also known as the Heaviside function, and it is used to model discontinuous events or processes. The step function is defined as follows:

h(x) = {

0, if x ≤ 0

1, if x > 0

## What is Unit Step?

Unit step is a mathematical function that produces a discontinuous pulse at its single argument. It is also known as the Heaviside function, after its discoverer, Oliver Heaviside.

## Derivative of Step Function

The derivative of the step function is the derivative of the function at 0.

## Integral of Step Function

The integral of a step function is the area under the curve.

## Unit Step Function Graph

A step function is a discontinuous function that has a sharp rise or fall. It is represented by a graph that looks like a staircase.

## Properties of Step Function

- A step function is a discontinuous function.
- A step function is a function that has a jump discontinuity at one or more points.
- A step function is a function that is continuous except at isolated points where it has a jump discontinuity.
- A step function can be represented by a graph that has a series of horizontal lines segments.