5 Easy Steps to Cut a Graph in Desmos

When it comes to graphing complex functions and equations, Desmos has emerged as a powerful tool for students and professionals alike. One of the key features that sets Desmos apart is its ability to manipulate graphs interactively, including cutting them into sections. Whether you’re trying to analyze different sections of a graph or simply want to isolate a specific region, knowing how to cut a graph in Desmos can greatly enhance your workflow.

To get started, select the graph you wish to cut. You can do this by clicking on the graph’s name in the sidebar or by clicking directly on the graph itself. Once the graph is selected, hover your mouse over any point on the graph and click. A small black circle will appear at the point where you clicked. This circle represents the cutting point.

To make the cut, simply drag the black circle to the desired location on the graph. As you drag, a dashed line will appear, indicating the proposed cut. Once you’re satisfied with the cut’s position, release the mouse button. The graph will now be cut into two separate sections, each of which can be manipulated independently. You can continue to make additional cuts as needed, allowing you to isolate specific regions or create complex geometric shapes.

Navigating the Desmos Interface

Desmos is a powerful online graphing calculator that provides various tools and features to create, analyze, and interact with graphs. To cut a graph in Desmos, you first need to become familiar with its user-friendly interface.

Getting Started with Desmos

To access Desmos, simply visit the website (www.desmos.com) or download the app on your device. Once you open the application, you will be presented with a blank canvas where you can start creating graphs.

The interface consists of several key elements:

• Graphing Panel: This is the central area where you plot and manipulate graphs.
• Toolbar: Located at the top, the toolbar provides access to various tools, such as the function editor, graphing options, and zoom controls.
• Sidebar: On the right side, the sidebar contains a list of saved graphs, settings, and additional features.
• Status Bar: Found at the bottom, the status bar displays information about the current graph and provides shortcuts for common actions.

Selecting the Appropriate Cutting Function

Desmos offers a range of cutting functions that enable you to slice a graph into multiple segments. Choosing the appropriate function depends on the specific properties of your graph and the desired cut regions.

Linear Cutting Functions

Linear cutting functions, such as vertical lines (x = k) and horizontal lines (y = k), create straight cuts that divide the graph into two or more linear segments. They are suitable for dividing the graph into rectangular regions or extracting specific sections based on their x- or y-coordinates.

Polynomial Cutting Functions

Polynomial cutting functions, such as parabolas (y = a(x – b)^2 + c) and ellipses (x^2/a^2 + y^2/b^2 = 1), create curved cuts that define regions of different shapes and sizes. They are particularly useful for isolating areas of interest or removing unwanted portions of the graph.

Advanced Cutting Functions

Desmos also offers advanced cutting functions, such as inequalities (y > mx + b), which create regions bounded by a certain condition. These functions allow for more complex slicing operations and are useful for isolating areas based on their slope or other mathematical properties.

The following table summarizes the different cutting functions available in Desmos:

Function	Cut Type	Suitable Scenarios
Vertical Line (x = k)	Straight, vertical	Dividing graph by x-coordinate
Horizontal Line (y = k)	Straight, horizontal	Dividing graph by y-coordinate
Parabola (y = a(x – b)^2 + c)	Curved, parabolic	Isolating specific regions
Ellipse (x^2/a^2 + y^2/b^2 = 1)	Curved, elliptical	Creating circular or elliptical regions
Inequality (y > mx + b)	Bounded by condition	Isolating regions based on slope or other properties

Creating Vertical Cuts

Vertical cuts slice the graph vertically, often used to isolate specific x-values or create vertical asymptotes. To create a vertical cut:

1. Click on the “Insert” tab in the top toolbar.
2. Choose “Cut” from the dropdown menu.
3. Select “Vertical” in the “Cut Direction” options.
4. Enter the x-value where you want the cut to occur. For example, to cut at x = 3, enter 3 in the “x-Intercept” field.
5. Click “OK” to create the vertical cut.

The vertical cut will appear as a vertical line on the graph, dividing it into two vertical regions. The graph will be discontinuous at the x-value of the cut, and the cut line will appear dashed or dotted to indicate discontinuity.

Example

To demonstrate, let’s say we have the graph of the function f(x) = 1/(x-2). If we want to create a vertical cut at x = 2, we would:

* Click “Insert” > “Cut”.
* Select “Vertical”.
* Enter 2 in the “x-Intercept” field.
* Click “OK”.

The graph will be cut at x = 2, isolating the points to the left of the cut from those to the right. The graph will also become discontinuous at x = 2, as the function is undefined at that value.

Establishing Horizontal Cuts

To establish horizontal cuts, follow these steps:

1. Locate the “Equation” field at the top of the Desmos workspace.
2. Click on the field and enter the equation you want to plot.
3. Select the “Add Slider” option from the left-hand toolbar.
4. In the “Slider” dialog box, enter a name for the slider (e.g., “y-Intercept”).
5. Set the minimum and maximum values for the slider (e.g., -10 and 10).
6. Set the initial value for the slider (e.g., 0).
7. Click “OK” to create the slider.
8. Enter the following equation in the “Equation” field:
   

   Equation
   f(x) – y-intercept

9. Replace “f(x)” with your original equation.
10. Replace “y-intercept” with the name of the slider you created (e.g., “y-Intercept”).
11. This will create a new graph that represents the original equation shifted vertically by the value of the slider.
12. Adjust the slider to observe how the graph moves vertically.

Utilizing Intersections and Cross-Sections

Intersection points are points where two or more graphs cross. To cut a graph using an intersection point, you can use the intersect() function. This function takes two graphs as arguments and returns a list of the points where the graphs intersect. You can then use these points to create a new graph that is cut at the intersection points.

Cross-sections are planes that intersect a three-dimensional graph. To cut a graph using a cross-section, you can use the crossSection() function. This function takes a graph and a plane as arguments and returns a new graph that is cut by the plane. The plane is defined by its normal vector and its distance from the origin.

Here is a table summarizing the key differences between intersection points and cross-sections:

Intersection Point	Cross-Section
Occurs where two or more graphs cross	Occurs where a plane intersects a three-dimensional graph
Can be found using the intersect() function	Can be found using the crossSection() function
Results in a new graph that is cut at the intersection points	Results in a new graph that is cut by the plane

### Examples

Here is an example of how to use the intersect() function to cut a graph:

“`
import desmos
graph1 = desmos.Graph(y=x^2)
graph2 = desmos.Graph(y=2x-1)
intersection_points = graph1.intersect(graph2)
new_graph = desmos.Graph()
for point in intersection_points:
new_graph.add(point)
“`

This code will create a new graph that is cut at the intersection points of the two original graphs.

Here is an example of how to use the crossSection() function to cut a graph:

“`
import desmos
graph = desmos.Graph(x^2 + y^2 + z^2 = 1)
plane = desmos.Plane(x=1)
cross_section = graph.crossSection(plane)
“`

This code will create a new graph that is cut by the plane.

Using Line Equations to Define Cuts

Line equations can be used to define cuts in Desmos. A cut is a line that divides the graph into two regions. The line equation must be in the form y = mx + b, where m is the slope and b is the y-intercept.

To create a cut using a line equation, follow these steps:

1. Click on the “Cuts” tab in the Desmos toolbar.
2. Click on the “Add Cut” button.
3. Enter the line equation in the text field.
4. Click on the “Create” button.

The line will now be added to the graph as a cut. The regions on either side of the cut will be shaded differently

Tips for Using Line Equations to Define Cuts

Here are some tips for using line equations to define cuts in Desmos:

• The line equation must be in the form y = mx + b.
• The slope (m) determines the steepness of the line.
• The y-intercept (b) determines where the line crosses the y-axis.
• You can use the “Intersect” tool to find the points where the line intersects the graph.
• You can use the “Shade Below” or “Shade Above” tools to shade the regions on either side of the cut.

Slope (m)	Y-Intercept (b)	Example Equation
0	0	y = 0
1	0	y = x
-1	0	y = -x
0	1	y = 1

Combining Multiple Cuts for Complex Shapes

Desmos allows you to combine multiple cuts to create complex shapes. The key is to use the intersection and union operators, denoted by the symbols ⋂ and ⋃, respectively.

Logical Operators

Operator	Description
⋂	Intersection
⋃	Union

The intersection operator creates a new graph that includes only the points that are common to both of the original graphs. The union operator creates a new graph that includes all the points from both of the original graphs.

Example

Suppose you want to create a graph that consists of a circle with a radius of 2 and a square with side length 4. To do this, you can use the following steps:

1. Graph the circle: (x – 0)^2 + (y – 0)^2 = 4
2. Graph the square: -2 ≤ x ≤ 2 and -2 ≤ y ≤ 2
3. Use the intersection operator to create a new graph that includes only the points that are common to both the circle and the square: (x – 0)^2 + (y – 0)^2 = 4 ⋂ (-2 ≤ x ≤ 2 and -2 ≤ y ≤ 2)

The resulting graph will be a circle with a square “cut out” of it.

Customizing Cut Parameters for Precision

To fine-tune the precision of your cuts, Desmos provides several adjustable parameters.

Vertical Cut Parameters

When creating a vertical cut, you can specify the following parameters:

• Cut at x =: The x-coordinate of the vertical line that defines the cut.
• Include Left: Whether to include the points to the left of the cut line in the resulting graph.
• Include Right: Whether to include the points to the right of the cut line in the resulting graph.

Horizontal Cut Parameters

Similarly, for a horizontal cut, you can specify the following parameters:

• Cut at y =: The y-coordinate of the horizontal line that defines the cut.
• Include Below: Whether to include the points below the cut line in the resulting graph.
• Include Above: Whether to include the points above the cut line in the resulting graph.

Advanced Precision Settings

For even more control, Desmos offers advanced precision settings:

Setting	Description
Cut Tolerance	The maximum distance that a point can be from the cut line and still be included in the graph.
Minimum Segments	The minimum number of segments that will be used to represent each curve in the resulting graph.

By adjusting these advanced settings, you can optimize the balance between precision and performance, ensuring that your graphs are accurate and visually appealing.

Uncutting a Graph for Revision

Recovering a Cut Graph

Once you’ve cut a graph in Desmos, you may realize that you need to remove the cut and restore the original graph. Here’s how to do it:

1. Select the graph you want to uncut.
2. Click on the “Cut” tool in the toolbar.
3. Hover over the graph’s edge where the cut was made.
4. Click on the “Uncut” button that appears.

Uncutting a Graph in Code

You can also uncut a graph using the Desmos Graphing Calculator’s code editor:

1. Click on the “Code” tab in the top-right corner of the screen.
2. Locate the line of code that defines the cut graph. It will look something like this:

f = cut(g, "x > 0")

3. Delete the cut() function from the code.
4. The graph will be restored to its original state.

Remember that uncutting a graph will permanently remove the cut and any modifications made to the cut regions. If you need to preserve the cut, you should duplicate the graph before making any changes.

Here’s a table summarizing the steps for uncutting a graph:

Method	Steps
Graphical Interface	Select the graph. Click the “Cut” tool. Hover over the cut edge. Click the “Uncut” button.
Code Editor	Open the “Code” tab. Locate the cut() function. Delete the cut() function.

Exporting and Saving Your Cut Graph

Once you have cut your graph, you can export or save it for future reference or to share with others. Here’s how:

1. Exporting Your Cut Graph

To export your graph as an image, click on the “Export” button in the top right corner of the Desmos graph window. A menu will appear with four options:

• PNG: Portable Network Graphics, suitable for web use.
• SVG: Scalable Vector Graphics, suitable for editing and printing.
• PDF: Portable Document Format, suitable for printing.
• CSV: Comma-Separated Values, suitable for data analysis.

Select the desired export format and click “Export.” You will be prompted to save the file to your computer.

2. Saving Your Cut Graph

To save your cut graph as a Desmos activity, follow these steps:

1. Click on the “File” menu in the top left corner of the Desmos window.
2. Select “Save Activity.” A window will appear with several options.
3. Enter a name for your activity.
4. Select a visibility option (Public, Private, or Shared with Link).
5. Click “Save.” Your graph will be saved in your Desmos account.

3. Sharing Your Cut Graph

To share your cut graph as a Desmos activity, follow these steps:

1. Save your graph as an activity (see steps above).
2. Click on the “Share” button in the top right corner of the Desmos window.
3. Choose the desired sharing option (Link, QR Code, Email, etc.).

4. Embedding Your Cut Graph

To embed your cut graph in a website or blog, follow these steps:

1. Save your graph as an activity (see steps above).
2. Click on the “Embed” button in the top right corner of the Desmos window.
3. Copy the provided code and paste it into the HTML code of your website or blog.

5. Troubleshooting

If you encounter any issues while exporting or saving your cut graph, check the following:

• Make sure your internet connection is stable.
• Try a different browser or clear your browser’s cache and cookies.
• Contact the Desmos support team for assistance.

How to Cut a Graph in Desmos

Desmos is a free online graphing calculator and interactive mathematics tool. It allows users to create, explore, and share graphs of functions, equations, and data. One of the features of Desmos is the ability to cut a graph, which means to divide it into two or more segments.

To cut a graph in Desmos, follow these steps:

1. Open Desmos and create or import the graph you want to cut.
2. Click on the graph to select it.
3. Click on the “Edit” menu in the top right corner of the screen.
4. Select “Cut Graph.”
5. A dialog box will appear asking you to specify a value for the cut point.
6. Enter the value of the cut point and click “OK.”

The graph will be cut into two or more segments at the specified cut point. You can continue to edit and manipulate each segment independently.

People Also Ask

How do you cut a graph at a point in Desmos?

To cut a graph at a specific point, enter the coordinates of the point in the “Cut Graph” dialog box.

How do you cut a graph vertically in Desmos?

To cut a graph vertically, enter a vertical line equation in the “Cut Graph” dialog box.

How do you cut a graph horizontally in Desmos?

To cut a graph horizontally, enter a horizontal line equation in the “Cut Graph” dialog box.