FAQs

To plot points, you can type one point per line, multiple points in the same line, or list them all in a table. To get started, try typing a coordinate pair in the expression list, such as \((2,1)\).

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• Graphing and Connecting Coordinate Points
• Coordinate Points Example Graph

To connect points, you can use a table or the polygon function.

To get started with a table, enter your point values. Then, click and hold the Color icon to open the Options menu. Toggle Line to connect the points.

To use the polygon function, type polygon\(\mathbf{(x_1,y_1)}\), where \(x_1\) is the \(x\)-column header and \(y_1\) is the \(y\)-column header. If the table consists of only two coordinates, this will connect them with a line. Otherwise, it will generate a closed polygon using the coordinates as vertices.

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• Graphing and Connecting Coordinate Points
• Connecting Points Example Graph

Enter the equation of the line you would like to see graphed. For example, try \(y=2x+3\). You can also enter equations that are not solved for \(y\), such as \(3x-4y=1\).

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• Linear Equations Example Graph

If you click anywhere on a line or curve, gray dots will appear at intercepts, intersection points, maximums, and minimums. Click a gray dot to display the coordinates at that point. Click the dot again to hide the coordinates.

To see coordinates on a curve, it's best to enter the expression explicitly. Coordinates are not displayed for parametric equations or in the 3D Calculator.

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• Important Points Example Graph

To enter a fraction, try using the Forward Slash (/) symbol on your keyboard or the Division operator (÷) in the on-screen keypad.

To convert an answer from a decimal to a fraction, click Convert.

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• Fractions Example Graph

To insert a table, type table in an expression line. Or, click Add Item and then Table.

You can also create a table from an expression line that contains:

• A single point such as \((1,0)\)

• A list of points separated by commas, such as 

  \((1,0)\), \((2,0)\), \((3,2)\), \((4,3)\)
• A function in function notation, such as \(f(x)=sin(x)\)

For each of these instances, click Edit List and then click Convert to Table .

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• Tables
• Tables Example Graph

If you're logged into your account in the Graphing Calculator, Geometry Tool, 3D Calculator, or Notebook, press the Share.

You’ll have the option to share your graph or notebook or a snapshot to the file. For notebooks, you’ll have additional options to control whether people can edit the contents.

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• Saving and Sharing Your Work

To limit the domain or range (\(x\)- or \(y\)- values) of a graph, add a restriction to the end of your equation in curly brackets {}. For example, \(y=2x\){\(0\)\(\lt\)\(x\)\(\lt\)\(3\)} would graph the line \(y=2x\) only for \(x\) values between \(0\) and \(3\)

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• Inequalities and Restrictions
• Restrictions Example Graph

To shade portions of your graph, replace the equal sign with an inequality sign. Try using <,>, ≤, or ≥ to explore how the shading changes with different inequality symbols.

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• Inequalities and Restrictions
• Inequalities Examples Graph

To graph a piecewise function, use the following syntax: \(y=\){condition: value, condition: value, etc.}

For example, \(y=\){\(x\)\(\lt\)\(0\):\(sin(x)\), \(x\)\(\ge\)\(0\):\(2x\)} will graph \(y=sin(x)\) for \(x\)-values less than \(0\) and \(y=2x\) for \(x\)-vlaues greater than or equal to \(0\).

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• Piecewise Example Graph

To adjust the viewing window, click Zoom In and Zoom Out.

For more precise control, you can also manually define the bounds of the viewport. Click Graph Settings and then adjust your separate axes.

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• Graph Settings

When you add data to a table, you can click Zoom Fit to automatically adjust the viewing window to fit your data.

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• Graph Settings
• Zoom Fit Example Graph

Open the Graph Settings menu to toggle between Radians and Degrees.

The Graphing and 3D Calculators default to radians, while the Geometry Tool and Scientific Calculator default to degrees.

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• Graph Settings

From the Options menu, you can change the line or point style, line thickness, change colors, and more. Open the menu with any of the following methods:

• Click and hold the Color icon
• Pressing Ctrl+Shift+O while focused in the expression
• Press Shift and then click the icon

You can define custom colors using the rgb, hsv, okhsv, oklab, and oklch functions.

You must assign a variable name to each custom color. It will then be available to select from the color list in the Options menu.

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• Custom Colors
• Custom Colors Example Graph

To add an image to your graph, click Add Item and then Image. Alternatively, you can drag an image from your desktop directly into the expression list.

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• Add an Item to a Graph

Create lists in Desmos using square brackets. For example, \(L=[1,2,3,4,5]\).

You can also create lists with evenly spaced elements using ellipses. For instance, \([1...10]\) generates a list of integers from 1 to 10, and \([1,3...11]\) creates a list of the odd integers from 1 to 11. You can use lists anywhere in an expression where you would use a number.

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• Lists
• Lists Example Graph

Start creating animations by attaching an image or graph object to a slider. Sliders allow you to play through different values for a variable, where you can control their speed, direction, and bounds.

For more advanced animations, explore actions and tickers. To get started, you must first enable actions at the account level. When signed in, click your account name to open the Account Settings page. Click Advanced and then check Actions.

Actions can update variable values, append lists, and more. The ticker can run actions over a specified time interval.

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• Sliders and Movable Points in a Graph
• Actions
• Race Car Example Graph

The tone function takes a required frequency input and an optional gain input. For the frequency, you can choose a value between \(20\) Hz to \(20000\) Hz, though they might not all be audible. We recommend starting with frequencies between \(110\) Hz and \(880\) Hz.

Gain is a multiplier on the amplitude of the sound wave. Larger amplitudes sound louder to our ears. You can set the gain between \(0\) and \(10\) depending on the frequency, but we recommend staying between \(0\) and \(1\).

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• Tone
• Introduction to Tone Example Graph

A recursive sequence is defined when the value of a term depends on one or more other terms in the sequence.

For example, consider the sequence 3,5,7,9,11,... where each term is 2 more than the previous one. In function notation, we can represent this as \(f(n) = f(n-1) + 2\). To specify where to start, set a base case for the first term, such as \(f(1)=3\).

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• Recursion
• Advanced Recursion Techniques

Sometimes, the calculator may determine that an equation is too complex to plot accurately within a reasonable amount of time. In such cases, the equation is plotted at a lower resolution.

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• Unresolved Detail Example Graph

To change the email address associated with your account, click your name and open Account Settings.

In the Profile Information tab, choose Change Email Address. This will send a link to the email address currently associated with your account.

If you receive an error message saying, you already have a Desmos account with that email address. Please reach out to us at support@desmos.com, and we'll be happy to help merge your accounts.