Graphing piecewise function calculator | Piecewise function grapher

Graphing piecewise function calculator

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Graphing a piecewise function can be a tedious and difficult task. Therefore, here we put at your disposal the Graphing piecewise function calculator, with which you can graph piecewise functionsquickly and easily.

To use the Piecewise function calculator you must follow the following steps:

  1. Indicate the number of pieces of the function you want to graph.
  2. Enter the mathematical expressions for each piece along with their respective domains. You can select a different color for each of the pieces.
  3. Then press the “plot” button to get the graph of the piecewise function.
Piecewise function calculator - instructions

What is a piecewise function?

A piecewise function is a mathematical function that is defined by multiple sub-functions, each of which applies to a different part of the function’s domain. These sub-functions are defined on specific intervals or “pieces” of the domain, and together they create a complete function.

Piecewise functions are commonly used to represent mathematical models that have different behaviors or rules for different parts of their domain. For example, a piecewise function might represent the cost of a taxi ride, which could have different rates for different distances traveled. In this case, the function would have one rule (or sub-function) for distances within a certain range, and another rule for distances outside that range.


Piecewise function examples

Here are a few examples of piecewise functions:

  • The absolute value function: f(x) = |x| is a piecewise function because it has different rules for different parts of its domain. Specifically, f(x) = x if x is greater than or equal to 0, and f(x) = -x if x is less than 0.

f(x)={xx<0x0xf(x) = \begin{cases}- x&x<0\\ x&0\leq x\\\end{cases}
piecewise function example 01
  • The step function: f(x) = {1 if x is greater than or equal to 0; 0 if x is less than 0} is another example of a piecewise function.

f(x)={10x0x0f(x) = \begin{cases}1&0\leq x\\0&x\leq 0\\\end{cases}
piecewise function example 02

It has a value of 1 for all non-negative values of x, and a value of 0 for all negative values of x.


  • Here’s a slightly more complex example:
f(x)={sin(x)1<x2.5x2.5<x2x1f(x) = \begin{cases}\sin\left(- x\right)&-1<x\leq 2.5\\- x&2.5<x\\2&x\leq -1\\\end{cases}
piecewise function example 03

How to graph piecewise functions

Graphing a piecewise function involves plotting different parts of the function over the specified intervals.

Here are the general steps to graph a piecewise function:

  1. Identify the different intervals: A piecewise function is defined over different intervals, so the first step is to identify the intervals over which each part of the function is defined.
  2. Write the function for each interval: Write down the expression for the function over each interval, using the appropriate variables and constants.
  3. Plot the function over each interval: Once you have the expression for each interval, plot the function over that interval.
  4. Check for continuity: Make sure that the function is continuous at the boundary points of each interval. If it is not, you will need to add an open circle at the point to indicate a discontinuity.
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