Graphing Calculator: Essential Skills

The essential skills on getting started with the graphing calculator!

Add an Item

The expression list is for more than just expressions. You can use the Add Item menu to add an expression, note, table, folder, or image to your graph. To start, click on the "plus sign" and then choose the type of item you'd like to add to your graph. An example of each is below:

Add item Menu. Example of each type of item in the add item menu. Screenshot.

Adding an Image

Add images to your graph to use as a template for your graph, add text labels, or for a little pop of extra color! To add an image to your graph, start by opening the Add Item menu and choose Image. Clicking and dragging the image into the expression list is also supported in many browsers.

Add image. Screenshot.

 

Movie Ticket image with drag to resize. Screenshot.

To Move the image, click on the center point and drag the image to where you’d like to place it. To Resize the image, click and drag any one of the outer points surrounding the image. Dragging outwards to make the image larger and inwards to make it smaller.

Image of expression list to manually change coordinate of center. Screenshot.

Or, you can manually change the coordinate of the center point in the expression list. This will automatically move the image so that its center is at that new coordinate point. You can resize the image by adjusting the width and height. You can also adjust the angle or opacity of the image.

Image of the expression list of an image to change center point, angle, opacity. screenshot.

Click and long-holding the image icon will allow you to adjust the opacity and placement of the image.

Change the Color or Style of the Graph

To change the color or style of an expression, long-hold the colored icon to the left of the expression. Clicking the icon will hide or show the expression.

Toggle expression line on/off. Screenshot.

 

Clicking and holding the icon next to the expression will open the color and style menu.

Color/style menu. Screenshot.

 

Lines

Line style menu. Screenshot.

Tables

Table style menu. Screenshot.

Points

Point style menu. screenshot.

 

You have the option to change the opacity and thickness of lines, points and labels by adjusting these values in the color/style settings.

Changing the opacity and thickness. Screenshot.

Convert a Function to a Table

Expressions and points can be shown as tables using Convert to Table. To start, click the Edit List button. If the expression line contains an available expression, a Convert to Table button will appear. Click on it to transform the expression line to a table.

Changing the opacity and thickness. Screenshot.

 

Equations, expressions, points, and lists of points can be converted to a table.

Single Point

Point converted to a table. Screenshot.

List of Points

List of points converted to a table. Screenshot.

Function Notation

Function converted to a table. screenshot.

 

Note: Convert to Table isn't available for Implicit expressions, parametric, and polar graphs.

Domain and Range Restrictions

Use curly braces at the end of an expression to add a domain or range restriction in seconds. From piecewise functions and implicit relations, to including sliders within your restrictions, Desmos makes it easy to control what you see in the coordinate plane. Get started with the video on the right, then dive deeper with the resources and challenges below.

Restriction showing y=2x\left\{1<x<3\right\}. Animation.

To limit the domain or range (x or y values of a graph), you can add the restriction to the end of your equation in curly brackets {}. In the example graph below the line y=2x is restricted for x values between 1 and 3.

Graph showing y=x^{2}\left\{1<y<5\right\}. Screenshot.

You can also use restrictions on the range of a function and any defined parameter.

Graph showing x^{2}+y^{2}\le20\left\{x<0\right\}\left\{y>0\right\}. Screenshot.

It's also possible to add multiple restrictions to the same expression line regardless of what parameter is being restricted.

 

Restrictions in Action

"The best way to learn is to do." – Paul Halmos

Interactive tour logo.  Screenshot.

Interactive Tour

Master the basics with a quick, step-by-step walkthrough.

Graphing Challenge logo.  Screenshot.

Graphing Challenges

Stretch your skills with graphing challenges.

Example graph logo. Screenshot.

Example Graphs

Learn more by exploring example graphs.

Represent a Fraction

To enter a fraction, try using the "/" symbol on the device keypad. Or, you can use the Desmos keypad.

Fraction symbol on the keypad. Screenshot.

 

To convert a decimal to a fraction use the icon to the left of the expression line in the graphing calculator and on the right in the scientific and four function calculators.

Decimal convert to fraction toggle. Screenshot.

Inequalities

Use inequalities to automatically shade above or below lines and curves. Combine implicit relations and inequalities to share the interior of a circle, or the concave part of a hyperbola. Add extra life to your Desmos math art with a bit of inequality-based shading. Get started with the video on the right, then dive deeper with the resources and challenges below.

With inequalities, you can add colored shading to your Desmos graph. Use strict inequalities (\(\lt and \gt \)) for dotted lines and non-strict inequalities (\(\le and \ge \)) for a solid line.

Showing graph of three shaded regions.  Line 1: x^{2}+y^{2}<4. Line 2:y\ge2x+10. Line 3: y\le2x-10. Screenshot.

 

For more intricate graphs, you can also use inequalities with restrictions to shade selected parts of the graph.

Showing graph of three shaded regions.  Line 1: y>x^{2}+2\left\{y<4\right\}. Line 2:-6\le x\le-2\left\{-1<y<1\right\}. Line 3: 0\le y\le2x-4\left\{x<4\right\}. Screenshot.

Inequalities in Action

"The best way to learn is to do." – Paul Halmos

Graphing challenge logo. Screenshot.

Graphing Challenges

Stretch your skills with graphing challenges.

Example graph logo. Screenshot.

Example Graphs

Learn more by exploring example graphs.

Lists

Define a list of values and calculate the mean, median, or standard deviation. Or use one or more lists to quickly plot a series of points, lines, or curves. Think of lists as the “two birds with one stone” feature in Desmos. Begin simply, and get as complex as you like. Get started with the video on the right, then dive deeper with the resources and challenges below.

You can make lists in Desmos using square brackets like this:

Image of a list with five elements. Screenshot.

 

You can create lists with evenly spaced elements. [1,...,10] is a list of the integers between 1 and 10. [1,3,...,11] is a list of the odd integers between 1 and 11. Table columns are available as lists in the rest of the system.

You can use lists anywhere in expressions that you would use a number.

Image of a list being used in an expression. Screenshot.

 

If L is a list, you can refer to the first element of L with L[1], produce a list of the first, third, and fifth elements of L with L[1,3,5], produce a list of the third through fifth elements of L with L[3...5], and produce a list of the third through last elements of L with L[3...]. If M is also a list, then L[M] produces a list of the elements of L given by the indices in M. You can also select the elements of a list that satisfy a condition: for example, if L is a list, then L[L>0] selects the positive elements of L, and L[mod(L,2)=0] selects the even elements of L.

 

Lists in Action

"The best way to learn is to do." – Paul Halmos

Interactive tour logo. Screenshot.

Interactive Tour

Master the basics with a quick, step-by-step walkthrough.

Graphing Challenge logo. Screenshot.

Graphing Challenges

Learn more by exploring example graphs.

Example graph logo. Screenshot.

Example Graphs

Learn more by exploring example graphs.

Piecewise Functions

To write a piecewise function, use the following syntax: y = {condition: value, condition: value, etc.} For example:

Expression line: y=\left\{x<0:\sin\left(x\right),x\ge0:2x\right\}. Screenshot.

 

See an example of the graph here .

Graph of y=\left\{x<0:\sin\left(x\right),x\ge0:2x\right\}. Screenshot.

Points of Interest

If you click a curve or expression, you'll see gray dots appear at interesting points including maximums, minimums, intercepts, and intersections. Click on a gray dot to open the coordinates at that point - click the point again to hide the coordinates. You can also trace along a function by clicking and dragging along the curve.

GIF clicking on the curve of the graph and pinning the points of interest on the screen. Animation.

Help Menu

See all of our tours and resources by clicking on the help menu Question Mark icon in the top right corner of any graph. Learn more about the Help Menu .

Calculator Help Center Menu. Screenshot.

Language Settings

To change the language of the calculator, click the world icon and select your language from the list.

Language Settings Menu. Screenshot.

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