Unit Step Function
Unit Step Function is yet another type of function used a lot in Signals and systems studies. It is defined as,
This function has no value at x = 0. It is called a step function because, at t = 0, it takes a step from 0 to 1. The domain for this function is R – {0} and range {0,1}.
Piecewise Function
Piecewise Function is a function that behaves differently for two types of input. As we know a function is a mathematical object which associates each input with exactly one output. For example: If a function takes on any input and gives the output as 3. It can be represented mathematically as f(x) = 3. But in the case of the Piecewise function, it is defined by individual expressions for each interval.
A piecewise function is defined across different intervals, each with its own specific function rule. A well-known example of such a function is the absolute value. Other examples of piecewise functions include the Heaviside step function, the rectangle function, and the triangle function, each characterized by distinct behaviors over their respective intervals.
In this article, we will study about piecewise function, how to graph a piecewise function, and how to evaluate it.
Piecewise Function
Table of Content
- What is Piecewise Function?
- Piecewise Function Definition
- Domain and Range of Piecewise Function
- Piecewise Function Graph
- Piecewise Function Examples
- Modulus Function
- Greatest Integer Function or Floor Function
- Least Integer Function or Ceiling Function
- Unit Step Function
- Signum Function
- Evaluating Piecewise Functions
- Piecewise Continuous Function
- Piecewise Continuous Function Graph
- Piecewise Function Worksheet