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

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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 long-hold the icon in the y-column header to open the options menu and enable the “Lines” toggle to connect the points. To use the polygon function, type \(polygon(x_1, y_1)\), 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 on a gray dot to display the coordinates at that point; click the dot again to hide the coordinates.

Note: 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 "/" symbol on your keyboard or the division operator (÷) in the Desmos on-screen keypad.

To convert an answer from a decimal to a fraction, click the icon to the left of the expression line.

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• Fractions Example Graph

To insert a table, simply type table, or use the Add Item menu (the plus sign in the top left of the expression list) and select Table.

• 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 the Edit List button at the top right of the expression list and then click the table icon next to the expression, which says Convert to Table or Create Table.

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• Tables
• Tables Example Graph

If you're logged into your account in the Graphing Calculator, Geometry Tool, or 3D Calculator, you can press the Share button in the upper right. This will generate a unique URL that refers to the current graph state, as well as other options for sharing your graph.

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• Saving and Managing Graphs

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, use the plus and minus signs in the top right corner of your window to zoom in and out

For more precise control, you can also manually define the bounds of the viewport. Adjust each axis separately in the Graph Settings menu, accessed using the wrench icon in the upper right corner.

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• Graph Settings

When you add data to a table, you’ll see the Zoom Fit icon in the bottom left corner of your expression. Click on the icon 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 by clicking the wrench in the upper right corner to find a radians/degrees toggle.

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

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• Graph Settings

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

• Long pressing the icon
• Pressing Ctrl+Shift+O while focused in the expression
• Shift + click the icon

Custom colors can be defined using the RGB or HSV color models, represented in Desmos by rgb and hsv functions that each take three input values to define a new color. RGB specifies the amounts of red, green, and blue in the color, while HSV specifies the hue, saturation, and value. Each custom color must be assigned a variable name in the expression list, and 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

Our community of users is continually discovering new ways to use Desmos as a canvas and outlet for creativity. Get started by creating your name with lines, or importing an image and tracing it with points and curves. Find inspiration from our Global Math Art Contest and explore the resources below.

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• Math Art
• Desmos Global Math Art Contest

To add an image to your graph, use the Add Item menu in the top left of the expression list and select Image. Alternatively, you can drag an image from your desktop directly into the expression list.

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• Add an Item

Desmos offers a range of accessibility features, including robust keyboard navigation, math-aware text-to-speech, audio trace, display enlargement, reverse contrast, braille mode, and more. Explore all the available features with the additional resources below.

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• Accessibility Page
• Keyboard Shortcuts

Reach out to us at accessibility@desmos.com with any questions or feedback.

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. Lists can be used anywhere in an expression where you would use a number.

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• Lists
• Lists Example Graph

A regression helps find a mathematical expression (like a line or a curve) to model the relationship between two sets of data, by approximating the value(s) of any undefined variables in the expression. Start by placing data into a table, then use the tilde symbol (~) to run a regression.

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• Regressions Article
• Regressions Tour

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 in the upper right corner and open the Account Settings page. Under the Advanced tab, check the Actions checkbox.

Actions can update variable values, append lists, and more. The ticker can run actions over a specified time interval. Learn more about sliders, actions, and the ticker with the resources below.

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• Sliders and Movable Points
• 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 20Hz to 20000Hz, though they might not all be audible. We recommend starting with frequencies between 110Hz and 880Hz.

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

Did you enter an expression in the Graphing Calculator and find that the resulting graph lacked some expected detail?

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 in the top right corner and select Account Settings.

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

If you receive an error message saying 'Sorry! Something went wrong. Please try again later,' it may indicate that 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.