How To Graph Piecewise Functions On Desmos
Welcome to a tutorial on how to graph piecewise functions on Desmos in the year 2023! Desmos is a powerful online graphing calculator that can be used to plot complex equations and functions. Piecewise functions are an important concept in mathematics, and Desmos allows you to easily graph them. In this article, we will walk you through the steps to graph piecewise functions on Desmos.
What are Piecewise Functions?
A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a different interval or domain. Piecewise functions are commonly used in mathematics to model real-world phenomena that have different behavior on different intervals or domains. For example, a piecewise function can be used to model the temperature of a room over time, where the temperature changes based on whether the heater is on or off.
Step 1: Enter the Equations
To graph a piecewise function on Desmos, you will need to first enter the equations for each sub-function. For example, consider the piecewise function:
f(x) = { x + 2 if x < 0; 2x - 1 if x >= 0 }
To enter this function into Desmos, you would need to split it into two sub-functions:
f(x) = x + 2 for x < 0
f(x) = 2x - 1 for x >= 0
Enter these equations into Desmos, one at a time, by clicking on the "+" icon in the top left corner of the screen and selecting "Function". Then, enter the equation in the text box that appears.
Step 2: Define the Domains
Next, you will need to define the domains for each sub-function. In our example, the first sub-function is only defined for x < 0, while the second sub-function is only defined for x >= 0. To define the domain for each sub-function, click on the wrench icon next to the equation and select "Domain". Then, enter the appropriate domain in the text box that appears.
Step 3: Graph the Function
Once you have entered the equations and defined the domains, you can graph the piecewise function by clicking on the "Graph" icon in the top left corner of the screen. The graph will show the different sub-functions on their respective domains.
Additional Tips
Here are some additional tips to help you graph piecewise functions on Desmos:
- Use parentheses around the domain to ensure that the function is only defined on the intended interval.
- If you need to add more sub-functions, click on the "+" icon and select "Function" again.
- If your piecewise function has more than two sub-functions, you can use the "add item" button in the domain settings to add additional domains.
Conclusion
Graphing piecewise functions on Desmos is a straightforward process that can be done in just a few steps. By entering the equations and defining the domains for each sub-function, you can create a clear and accurate graph that shows the behavior of the function on different intervals or domains. We hope that this tutorial has been helpful in teaching you how to graph piecewise functions on Desmos!
Happy graphing!
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