How To Make Piecewise Functions On Desmos
Desmos is a powerful online graphing calculator that lets you create complex mathematical functions with ease. One of the most useful features of Desmos is its ability to create piecewise functions. In this tutorial, we will show you how to make piecewise functions on Desmos in just a few simple steps.
Step 1: Open Desmos
The first step is to open Desmos in your web browser. You can do this by navigating to the Desmos website and clicking on the "Start Graphing" button. Once the calculator opens, you will see a blank canvas where you can start creating your function.
Step 2: Define Your Function
To begin creating your piecewise function, you first need to define the function itself. You can do this by typing the equation into the calculator, just like you would with any other function. For example, let's say we want to create a piecewise function that is equal to 2x + 4 when x is less than or equal to 3, and 3x - 1 when x is greater than 3. We would type the following equation into the calculator:
2x + 4, x ≤ 3
3x - 1, x > 3
Step 3: Add Your Function to the Graph
Once you have defined your function, you need to add it to the graph. To do this, click on the "+" icon in the top left corner of the screen and select "Function." This will open a new panel where you can enter your function. Simply copy and paste the equation you defined in Step 2 into the panel and click "Add" to add the function to the graph.
Step 4: Adjust the Domain
By default, Desmos will plot your function over the entire domain of x. However, for a piecewise function, you may want to restrict the domain to only include certain values of x. To do this, click on the wrench icon in the top right corner of the screen and select "Settings." Then, click on the "Restrict x/y to" dropdown menu and select "Custom." Here, you can set the domain of x by entering the minimum and maximum values you want to include.
Step 5: Add a Point of Discontinuity
If your piecewise function has a point of discontinuity, you will need to add it to the graph manually. To do this, click on the "+" icon again and select "Point." Then, click on the graph where you want to add the point.
Step 6: Add Labels and Styling
To make your graph easier to read, you can add labels and styling to your function. For example, you may want to add a label to indicate which part of the function corresponds to which equation. You can also change the color and style of your graph by clicking on the wrench icon and selecting "Color" or "Style."
Step 7: Save and Share Your Function
Once you have created your piecewise function, you can save it and share it with others. To save your function, click on the "Save" button in the top right corner of the screen. This will generate a unique URL that you can share with others. You can also export your graph as an image or a PDF by clicking on the wrench icon and selecting "Export."
Step 8: Practice and Experiment
The best way to get comfortable with making piecewise functions on Desmos is to practice and experiment. Try creating different functions with different domains, points of discontinuity, and styling. You may also want to explore some of the other features of Desmos, such as sliders and tables, that can make working with functions even more powerful.
Conclusion
Creating piecewise functions on Desmos is a great way to visualize complex mathematical functions. By following the steps outlined in this tutorial, you can easily create your own piecewise functions and share them with others. Remember to practice and experiment to get the most out of this powerful tool.
Happy graphing!
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