Piecewise Function
Define the Piecewise function in Maths.
A Piecewise function is a function that is defined for different sequences of intervals differently.
How do you write a Piecewise Function?
To write peicewise function, we need to write expression for each defined domaine individually. Let’s consider an example as follows:
OR
f(x) = 2x + 1, if x < 0
f(x) = x2, if 0 ≤ x < 2
f(x) = 5, if x ≥ 2
How to Graph a Piecewise Function?
To graph a peicewise function we need to plot the graph of each individual defined expression for given domain.
What is a Piecewise Continuous Function?
If the lower limit and the upper limit of successive sequence of function are same then a piecewise function is continuous. In other words, a piecewise function is continuous when the function is continuous in the entire domain of the given function.
What is a Differentiable Piecewise Function?
If the function is differentiable at all the boundary points as well in the entire domain, the piecewise function is called differentiable.
Give an Example of a Piecewise Linear Function.
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This is a piecewise linear function as its graph will be a straight line in all the three pieces.
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