How To Add Piecewise Functions In Desmos

Piecewise Functions Geogebra vs Desmos Mathleticism from mathleticism.net

Desmos is a powerful online graphing calculator that has become popular among students, teachers, and professionals in various fields. One of its useful features is the ability to graph piecewise functions, which are functions that have different formulas for different parts of their domain. In this tutorial, we will show you how to add piecewise functions in Desmos, step by step.

Step 1: Open Desmos

The first step is to open Desmos in your web browser. You can do this by typing "desmos.com" in the address bar and pressing Enter. Once the website loads, you will see a blank graphing canvas.

Step 2: Define the Functions

To add a piecewise function in Desmos, you need to define each part of the function separately. For example, let's say you want to graph the function f(x) = |x| for x ≤ 0 and f(x) = x^2 for x > 0. To do this, you would define two separate functions:

f(x) = |x|

and

g(x) = x^2

You can enter these functions in the input bar at the top of the Desmos screen, using the variable "x". For example, to enter the first function, you would type:

f(x) = |x|

and press Enter. Desmos will graph the function automatically.

Step 3: Combine the Functions

Now that you have defined the functions, the next step is to combine them into a single piecewise function. To do this, you need to use the "piecewise" command in Desmos. This command allows you to define different formulas for different parts of the function's domain.

To use the piecewise command, type "piecewise(" in the input bar, followed by the first formula, a comma, and the second formula. For example, to define the piecewise function for f(x) = |x| for x ≤ 0 and f(x) = x^2 for x > 0, you would type:

piecewise(x ≤ 0, |x|, x > 0, x^2)

and press Enter. Desmos will graph the piecewise function automatically, with the different formulas shown in different colors.

Step 4: Customize the Graph

Once you have added the piecewise function, you can customize the graph as desired. For example, you can change the color of each part of the function, add labels to the axes, and adjust the viewing window. To do this, use the options in the toolbar at the top of the Desmos screen.

You can also add more functions to the graph, by defining them separately and then combining them with the piecewise command. This allows you to create complex graphs that show multiple functions and their relationships.

Step 5: Save and Share the Graph

Finally, once you have created the graph you want, you can save it and share it with others. To save the graph, click on the "Save" button in the toolbar and choose a name and location for the file.

To share the graph, you can either send the file to others or share a link to the graph on the Desmos website. This allows others to view and interact with the graph online, without needing to have Desmos installed on their own computer.

Conclusion

Adding piecewise functions in Desmos is a simple process that can help you create complex graphs with multiple functions. By defining each part of the function separately and combining them with the piecewise command, you can create graphs that show the relationships between different parts of the function's domain. And with the customization and sharing options in Desmos, you can create and share graphs that are tailored to your needs and audience.

So, next time you need to graph a piecewise function, try using Desmos and see how easy and powerful it can be!

Source: mathleticism.net

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