# Graphing Calculator: Essential Skills

### The essential skills on getting started with the graphing calculator!

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 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.

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.

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.

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.

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

Lines

Tables

Points

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

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.

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

Single Point

List of Points

Function Notation

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.

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.

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

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

## Restrictions in Action

### Interactive Tour

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

### Graphing Challenges

Stretch your skills with graphing challenges.

### Example Graphs

Represent a Fraction

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

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.

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.

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

## Inequalities in Action

### Graphing Challenges

Stretch your skills with graphing challenges.

### 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:

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.

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

### Interactive Tour

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

### Example Graphs

Piecewise Functions

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

See an example of the graph here .

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.