Piecewise Function Graph
To graph the Piecewise Function, we just need to graph the function individually for all the different intervals it is defined.
Example: Plot the graph of the function defined as follows:
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Solution:
As the domain of the function is the complete set of real numbers, thus there is no such values in R for which the function is not defined.
Now, for the first piece of graph for x < -1, is given as f(x) = x, which can be easily plotted. So the graph of a function for x < -1 is a straight line with a slope of 1 that passes through the origin.
For the second piece of the graph for -1 ≤ x ≤ 2, the given function is a constant function as f(x) = 2. So the graph of a function for -1 ≤ x ≤ 2 is again a straight horizontal line which is at a 2 unit distance from the x-axis.
For the third piece of the graph for x > 2, the given function is a parabolic curve that opens upwards and x2 is a increasing and continuous function, so the graph starts at the point (2, 4) goes in the upward direction as parabolic curve.
Plot these three pieces of the graph to obtain the required graph of the function.
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