What is Piecewise Function?
Piecewise Function is a function that is defined differently on a sequence of intervals. In other words, a piecewise function is a mathematical function that is defined by multiple sub-functions, with each sub-function being valid only in a certain interval or region of the domain. In other words, a piecewise function is a function that is defined differently on different parts of its domain.
The general piecewise function can be written mathematically as:
Where,
- f1(x), f2(x), and f3(x) are three different functions, and
- a, b, and c are some real numbers.
The above expression for piecewise function means that for x less than a, the function takes on the value of f1(x), for x between a and b, it takes on the value of f2(x), and for x greater than or equal to b, it takes on the value of f3(x).\\
Piecewise Function Definition
A piecewise function, also known as a piecewise-defined function, is a function that is defined by different expressions or formulas on different intervals of its domain. This enables us to accurately describe functions that exhibit varying behaviors or properties within different ranges of input values.
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.
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