Piecewise features, combining a number of features over completely different intervals, can current challenges when graphing. Nevertheless, Desmos, an internet graphing calculator, provides a handy resolution. By using its piecewise perform capabilities, customers can effortlessly visualize the habits of those features throughout various domains. Whether or not you are a pupil finding out advanced equations or knowledgeable in search of to research real-world situations, Desmos empowers you to discover piecewise features with exceptional readability and precision.
To start graphing a piecewise perform in Desmos, outline every phase of the perform individually. As an example, if the piecewise perform is outlined as f(x) = x for x ≤ 0 and f(x) = x^2 for x > 0, you’ll first enter “x” within the equation editor for the interval x ≤ 0 and “x^2” for the interval x > 0. Desmos robotically acknowledges the piecewise nature of the perform, displaying the graph accordingly.
Moreover, Desmos offers superior options for customizing and analyzing piecewise features. You’ll be able to regulate the area and vary of the graph, zoom out and in to give attention to particular intervals, and add labels and annotations to boost comprehension. By harnessing these capabilities, you’ll be able to acquire a deeper understanding of the habits of piecewise features, determine factors of discontinuity, and discover their purposes in numerous fields.
Graphing Piecewise Features on Desmos: A Step-by-Step Information
1. Understanding Piecewise Features
Piecewise features are a sort of perform that consists of a number of components, every of which is outlined over a particular interval. For instance, the next perform is a piecewise perform with two components:
$$f(x)=start{circumstances} x+1 & textual content{if } xle 0 x^2 & textual content{if } x>0 finish{circumstances}$$
The primary a part of the perform is outlined for $xle 0$, and the second half is outlined for $x>0$. The graph of a piecewise perform is solely the union of the graphs of its particular person components.
To graph a piecewise perform on Desmos, you’ll be able to comply with these steps:
- Enter the perform into Desmos. You are able to do this by typing the perform into the enter area on the prime of the display screen.
- Click on on the "Graph" button. This may generate a graph of the perform.
- Establish the completely different components of the perform. The graph of a piecewise perform could have a number of segments, every of which corresponds to a distinct a part of the perform.
- Label the completely different components of the perform. You need to use the "Textual content" instrument so as to add labels to the completely different components of the perform.
Right here is an instance of easy methods to graph a piecewise perform on Desmos:
[Image of a piecewise function graphed on Desmos]
The perform on this instance is outlined as follows:
$$f(x)=start{circumstances} x+1 & textual content{if } xle 0 x^2 & textual content{if } x>0 finish{circumstances}$$
The graph of the perform has two components: a linear half for $xle 0$ and a parabolic half for $x>0$. The 2 components of the graph are separated by a vertical line at $x=0$.
2. Utilizing the Piecewise() Operate
Desmos additionally offers a built-in perform known as Piecewise(), which can be utilized to graph piecewise features. The Piecewise() perform takes two arguments: an inventory of circumstances and an inventory of corresponding outputs. For instance, the next code would graph the identical piecewise perform as within the earlier instance:
Piecewise({
{x+1, x<=0},
{x^2, x>0}
})
The primary argument to the Piecewise() perform is an inventory of circumstances. Every situation is a logical expression that determines whether or not the corresponding output ought to be used. The second argument to the Piecewise() perform is an inventory of outputs. Every output is the worth of the perform for the corresponding situation.
The Piecewise() perform can be utilized to graph any piecewise perform. Nevertheless, it is very important observe that the circumstances should be mutually unique and exhaustive. Which means that every situation should be true for a distinct set of values, and the union of all of the circumstances should cowl the complete area of the perform.
3. Desk of Values
One other solution to graph a piecewise perform is to make use of a desk of values. A desk of values reveals the enter and output values of a perform for a given set of values. Right here is an instance of a desk of values for the piecewise perform from the earlier instance:
| x | f(x) |
|---|---|
| -2 | -1 |
| -1 | 0 |
| 0 | 1 |
| 1 | 1 |
| 2 | 4 |
The desk of values reveals that the perform takes the worth -1 when x=-2, the worth 0 when x=-1, the worth 1 when x=0, the worth 1 when x=1, and the worth 4 when x=2. These values can be utilized to plot the graph of the perform.
4. Graphing Strategies
There are a variety of various strategies that can be utilized to graph piecewise features. Among the most typical strategies embrace:
- Utilizing the Piecewise() perform
- Utilizing a desk of values
- Graphing every a part of the perform individually
- Utilizing a graphing calculator
The most effective method for graphing a piecewise perform is dependent upon the precise perform. Nevertheless, the Piecewise() perform is an effective choice for many piecewise features.
Understanding Piecewise Features
Piecewise features are a sort of perform that’s outlined by completely different guidelines for various intervals of the enter variable. Which means that the graph of a piecewise perform could have completely different sections, every of which is outlined by a distinct rule. Piecewise features are sometimes used to mannequin conditions the place the connection between the enter and output variables just isn’t linear.
For instance, take into account the next piecewise perform:
“`
f(x) =
{
x + 1 if x < 0
x^2 if x >= 0
}
“`
This perform is outlined by two completely different guidelines: one for when x is lower than 0 and one for when x is bigger than or equal to 0. The graph of this perform could have two sections: a line for x lower than 0 and a parabola for x better than or equal to 0.
Piecewise features will be graphed on Desmos utilizing the next steps:
| Step | Motion |
|---|---|
| 1 | Enter the perform into the Desmos graph. On this instance: `f(x) = x + 1, x < 0` `f(x) = x^2, x >= 0` |
| 2 | Click on on the “Graph” button. Desmos will graph the perform and present you the completely different sections. |
Listed here are some further ideas for graphing piecewise features on Desmos:
- Be certain that to enter the perform appropriately. Desmos is case-sensitive, so be certain that to make use of the right capitalization and punctuation.
- Use the “Area” and “Vary” sliders to regulate the viewing window. This will help you see the completely different sections of the graph extra clearly.
- Use the “Desk” instrument to see the values of the perform at completely different factors. This will help you confirm that the graph is right.
Making a Piecewise Operate on Desmos
Piecewise features are mathematical features which are outlined by completely different expressions over completely different intervals. They’re generally used to mannequin conditions the place the habits of the perform modifications abruptly at sure factors.
To create a piecewise perform on Desmos, you should use the next steps:
1. Open Desmos. Go to www.desmos.com and click on on the “Create” button.
2. Enter the perform. Within the perform entry area, enter the piecewise perform utilizing the next syntax:
“`
piecewise(condition1, expression1, condition2, expression2, …, default)
“`
the place:
* `condition1` is the situation that determines when `expression1` is evaluated.
* `expression1` is the expression that’s evaluated when `condition1` is true.
* `condition2` is the situation that determines when `expression2` is evaluated.
* `expression2` is the expression that’s evaluated when `condition2` is true.
* … (elective) Further circumstances and expressions will be added as wanted.
* `default` (elective) is the expression that’s evaluated when not one of the circumstances are true.
3. Instance: Graphing a piecewise perform with a number of circumstances
Let’s create a piecewise perform that’s outlined by the next expressions over completely different intervals:
“`
f(x) = {
x + 2, if x < 0
x^2, if 0 ≤ x < 2
x – 1, if x ≥ 2
}
“`
To graph this perform on Desmos, we are able to comply with these steps:
- Open Desmos and click on on the “Create” button.
- Enter the perform within the perform entry area utilizing the next syntax:
- Click on on the “Graph” button to generate the graph of the piecewise perform.
piecewise(x < 0, x + 2, 0 ≤ x < 2, x^2, x ≥ 2, x - 1)
The ensuing graph will present three distinct segments, every comparable to one of many expressions within the piecewise perform.
Here’s a desk summarizing the steps for graphing a piecewise perform with a number of circumstances:
| Step | Description |
|---|---|
| 1 | Open Desmos and click on on the “Create” button. |
| 2 | Enter the piecewise perform within the perform entry area utilizing the syntax: piecewise(condition1, expression1, condition2, expression2, …, default) |
| 3 | Click on on the “Graph” button to generate the graph of the piecewise perform. |
Defining Totally different Intervals for the Graph
To precisely graph a piecewise perform on Desmos, it’s essential to outline the completely different intervals over which each bit of the perform might be outlined. These intervals decide the vary of values for the impartial variable over which each bit of the perform is legitimate.
To outline intervals in Desmos, use the next syntax:
“`
area: [interval1, interval2, …]
“`
the place `interval1`, `interval2`, and many others., characterize the completely different intervals over which the perform is outlined.
Intervals will be outlined utilizing:
- Open intervals: `(a, b)`
- Closed intervals: `[a, b]`
- Half-open intervals: `[a, b)` or `(a, b]`
- Infinite intervals: `(-∞, a)`, `(a, ∞)`, `(-∞, ∞)`
For instance, if you wish to outline a piecewise perform that’s outlined over three intervals, you’ll use the next syntax:
“`
area: (-∞, 0), [0, 5], (5, ∞)
“`
This means that the primary piece of the perform is outlined over the interval `(-∞, 0)`, the second piece is outlined over the interval `[0, 5]`, and the third piece is outlined over the interval `(5, ∞)`.
Deciding on Appropriately Outlined Intervals for Totally different Piecewise Features
When defining intervals for piecewise features, it is very important select intervals which are applicable for the perform. For instance, if the perform is outlined for all actual numbers, you then would use the interval `(-∞, ∞)`.
Nevertheless, if the perform is simply outlined for a restricted vary of values, you then would want to decide on intervals that mirror these limitations. As an example, if the perform is simply outlined for optimistic numbers, you then would use the interval `(0, ∞)`.
It’s also vital to make sure that the intervals are disjoint, which means that they don’t overlap. If the intervals overlap, then the graph of the perform won’t be correct.
Instance: Defining Intervals for a Particular Piecewise Operate
Think about the next piecewise perform:
“`
f(x) = { x + 1, if x < 0
{ 0, if 0 ≤ x < 2
{ x – 1, if x ≥ 2
“`
To graph this perform on Desmos, you would want to outline three intervals:
“`
area: (-∞, 0), [0, 2), [2, ∞)
“`
The first interval, `(-∞, 0)`, represents the values of `x` for which the first piece of the function, `x + 1`, is defined. The second interval, `[0, 2)`, represents the values of `x` for which the second piece of the function, `0`, is defined. The third interval, `[2, ∞)`, represents the values of `x` for which the third piece of the function, `x – 1`, is defined.
| Interval | Piece of Function |
|---|---|
| (-∞, 0) | x + 1 |
| [0, 2) | 0 |
| [2, ∞) | x – 1 |
By defining these intervals, you can accurately graph the piecewise function on Desmos.
Plotting the Function on the Graph
To plot a piecewise function on Desmos, follow these steps:
- Navigate to the Desmos Graphing Calculator.
- Click on the “Create” tab.
- In the “Input” field, enter the piecewise function in the following format:
Syntax Example f(x) = {g(x), x < a}
{h(x), x ≥ a}f(x) = {x + 1, x < 0}
{x – 1, x ≥ 0} - Replace “g(x)” and “h(x)” with the appropriate expressions for each piece of the function.
- Replace “a” with the value of the breakpoint.
- Click on the “Graph” button to plot the function.
- Enter the piecewise() command into the Desmos calculator.
- Enter the conditions and expressions for each interval of the function.
- Click the "Graph" button.
- Transformations: Transformations can be used to move, scale, and rotate graphs. Desmos offers a variety of transformation commands, including translate(), scale(), and rotate().
- Polar Coordinates: Polar coordinates can be used to graph functions that are defined in terms of angles and distances. Desmos offers a polar() command that can be used to convert rectangular coordinates to polar coordinates.
- Implicit Functions: Implicit functions are equations that define a curve without explicitly solving for the dependent variable. Desmos offers an implicit() command that can be used to graph implicit functions.
- Parametric Equations: Parametric equations are equations that define a curve by specifying the coordinates of each point as a function of a parameter. Desmos offers a parametric() command that can be used to graph parametric equations.
- Inequalities: Inequalities can be used to shade regions of a graph. Desmos offers a shade() command that can be used to shade regions defined by inequalities.
- Click the "Custom Graph" button.
- Enter the equation for your graph.
- Click the "Graph" button.
- Interactive graphs: Desmos graphs are interactive, which allows students to explore mathematical concepts in a more hands-on way.
- Real-time feedback: Desmos provides real-time feedback, which helps students to identify and correct errors as they work.
- Collaboration tools: Desmos offers collaboration tools that allow students to work together on graphs and share their findings.
- Desmos Help Center: The Desmos Help Center provides a variety of documentation and tutorials on how to use Desmos.
- Desmos Blog: The Desmos Blog features articles on new features, tips and tricks, and lesson plans.
- Desmos Forum: The Desmos Forum is a community where users can ask questions and share ideas.
- Enter the equation for the first interval of the function into the Desmos equation editor.
- Click on the “Add Function” button to add a second function.
- Enter the equation for the second interval of the function into the equation editor.
- Click on the “Add Function” button to add a third function.
- Continue adding functions for each interval of the piecewise function.
- Once you have entered all of the functions, click on the “Graph” button.
- y = 2x
- y = 3x
- You can use the “Domain” and “Range” options in the “Graph Settings” menu to restrict the domain and range of the graph.
- You can use the “Color” option in the “Graph Settings” menu to change the color of the graph.
- You can use the “Legend” option in the “Graph Settings” menu to add a legend to the graph.
- arcsin(x) = y if sin(y) = x for -1 ≤ x ≤ 1 and -π/2 ≤ y ≤ π/2
- arccos(x) = y if cos(y) = x for -1 ≤ x ≤ 1 and 0 ≤ y ≤ π
- arctan(x) = y if tan(y) = x for all real numbers x and -π/2 < y < π/2
- arcsin(x):
- arccos(x):
- arctan(x):
- Simplify the equations. Earlier than plugging your piecewise features into Desmos, simplify the equations as a lot as attainable. This may cut back the variety of calculations that Desmos must carry out, bettering the graphing velocity.
- Use brackets. When defining the completely different items of your piecewise perform, at all times use brackets to group the phrases. This helps Desmos appropriately interpret the perform’s habits on completely different intervals.
- Keep away from nested piecewise features. Whereas Desmos can deal with nested piecewise features, they are often computationally costly. If attainable, attempt to simplify your piecewise perform right into a single expression with out nested piecewise features.
- Use the “optimize” command. Desmos offers an “optimize” command that may try to simplify your piecewise perform and enhance its graphing efficiency. To make use of this command, kind “optimize()” after your piecewise perform.
- Break down advanced piecewise features. In case your piecewise perform is especially advanced, attempt breaking it down into smaller items. Graph each bit individually after which mix the graphs utilizing the “mix” command.
- Cut back the variety of factors. In case your graph is just too gradual to load, attempt lowering the variety of factors that Desmos makes use of to generate the graph. You are able to do this by adjusting the “pattern charge” setting within the graph’s properties panel.
- Use the “cache” command. If you’re graphing the identical piecewise perform a number of occasions, think about using the “cache” command to retailer the graph in Desmos’s cache. This may stop Desmos from having to recalculate the graph every time, bettering the efficiency.
- Linear piecewise features
- Quadratic piecewise features
- Exponential piecewise features
- Logarithmic piecewise features
- Trigonometric piecewise features
Example
Let’s plot the following piecewise function:
f(x) = {x + 1, x < 0}
{x – 1, x ≥ 0}
To do this, we would enter the following into the Desmos Graphing Calculator:
f(x) = {x + 1, x < 0}
{x – 1, x ≥ 0}
Once we click on the “Graph” button, we would see the graph of the function plotted on the screen.
Exploring Advanced Graphing Techniques
1. Piecewise Functions on Desmos
Piecewise functions are a type of function that is defined differently for different intervals of the independent variable. In Desmos, you can define a piecewise function using the piecewise() command. The syntax for the piecewise() command is:
piecewise(condition1, expression1, condition2, expression2, ..., conditionn, expressionn)
where each condition is an equation or inequality that defines the interval for which the corresponding expression is evaluated.
2. Graphing Piecewise Functions
To graph a piecewise function in Desmos, simply follow these steps:
3. Advanced Graphing Techniques
In addition to the basic graphing techniques described above, Desmos also offers a number of advanced graphing techniques that can be used to create more complex graphs. These techniques include:
4. Creating Custom Graphs
In addition to graphing standard functions, Desmos also allows you to create custom graphs. To create a custom graph, simply follow these steps:
5. Saving and Sharing Graphs
Once you have created a graph, you can save it or share it with others. To save a graph, click the "Save" button. To share a graph, click the "Share" button.
6. Using Desmos in the Classroom
Desmos is a powerful tool that can be used to teach and learn mathematics. Desmos offers a variety of features that make it ideal for use in the classroom, including:
7. Desmos Resources
There are a number of resources available to help you learn more about Desmos. These resources include:
8. Advanced Graphing Techniques: Beyond the Basics
While the basic graphing techniques described above are sufficient for most purposes, there are a number of advanced graphing techniques that can be used to create more complex and informative graphs. These techniques include:
Using Tables and Lists: Tables and lists can be used to plot data points and create graphs. This can be useful for visualizing data or creating custom graphs.
Working with Multiple Functions: Desmos allows you to graph multiple functions on the same set of axes. This can be useful for comparing functions or solving systems of equations.
Using Graphing Themes: Desmos offers a variety of graphing themes that can be used to customize the appearance of your graphs. This can be useful for making your graphs more readable or visually appealing.
Creating Custom Legends: Desmos allows you to create custom legends for your graphs. This can be useful for identifying different functions or data sets.
Exporting Graphs: Desmos allows you to export your graphs in a variety of formats, including PNG, SVG, and PDF. This can be useful for sharing your graphs with others or using them in presentations.
By mastering these advanced graphing techniques, you can create more complex and informative graphs that will help you to better understand and communicate mathematical concepts.
Graphing Piecewise Exponential Functions
Piecewise exponential functions are a type of function that has different equations for different intervals of the input. These functions are often used to model situations where the rate of change changes at a certain point. For example, a piecewise exponential function could be used to model the population of a city that grows at a different rate before and after a certain year.
To graph a piecewise exponential function on Desmos, you can use the following steps:
Example
Consider the following piecewise exponential function:
| Interval | Equation |
|---|---|
| x ≤ 0 | y = 2x |
| x > 0 | y = 3x |
To graph this function on Desmos, you can enter the following equations into the equation editor:
Once you have entered both equations, click on the “Graph” button. The graph of the piecewise exponential function will be displayed.
Additional Notes
Here are some additional notes about graphing piecewise exponential functions on Desmos:
Graphing Piecewise Inverse Trigonometric Functions
Inverse trigonometric functions, also known as arcus functions, can be graphed piecewise using Desmos. These functions are defined as follows:
To graph an inverse trigonometric function on Desmos, follow these steps:
1. Open Desmos at desmos.com.
2. Click on the “Graph” tab.
3. In the input field, type the inverse trigonometric function you want to graph. For example, to graph arcsin(x), type “arcsin(x)”.
4. Click on the “Enter” key.
5. The graph of the inverse trigonometric function will be displayed.
Here are some examples of graphs of inverse trigonometric functions:
Graphing Piecewise Inverse Trigonometric Functions
Inverse trigonometric functions can also be graphed piecewise. For example, to graph the function,
“`
f(x) = {
arcsin(x), if x ≥ 0
-arcsin(x), if x < 0
}
“`
follow these steps:
1. Open Desmos at desmos.com.
2. Click on the “Graph” tab.
3. In the input field, type the following function:
“`
f(x) = {
arcsin(x), if x ≥ 0
-arcsin(x), if x < 0
}
“`
4. Click on the “Enter” key.
5. The graph of the piecewise inverse trigonometric function will be displayed.
Here is an example of a graph of a piecewise inverse trigonometric function:
Table of Inverse Trigonometric Functions
Here is a table总结summary of inverse trigonometric functions:
| Function | Domain | Range | Graph |
|---|---|---|---|
| arcsin(x) | [-1, 1] | [-π/2, π/2] | |
| arccos(x) | [-1, 1] | [0, π] | |
| arctan(x) | All actual numbers | [-π/2, π/2] |
Graphing Piecewise Mixtures
Combining Totally different Piecewise Definitions
In lots of circumstances, we have to graph piecewise features that encompass a number of completely different definitions. For instance, a perform could have one definition for x < 0, one other definition for 0 ≤ x < 2, and a 3rd definition for x ≥ 2.
To graph such a perform in Desmos, we are able to use the next steps:
1. Outline the primary piece of the perform utilizing the `piece()` perform. For instance:
“`
f1(x) = piece(x < 0, x^2)
“`
2. Outline the second piece of the perform utilizing the `piece()` perform. For instance:
“`
f2(x) = piece(0 ≤ x < 2, x + 1)
“`
3. Outline the third piece of the perform utilizing the `piece()` perform. For instance:
“`
f3(x) = piece(x ≥ 2, 2x – 3)
“`
4. Mix the three items of the perform utilizing the `if()` perform. For instance:
“`
f(x) = if(x < 0, f1(x), if(0 ≤ x < 2, f2(x), f3(x)))
“`
This may create a piecewise perform that has the definition of `f1(x)` for x < 0, the definition of `f2(x)` for 0 ≤ x < 2, and the definition of `f3(x)` for x ≥ 2.
Instance: Graphing a Operate with Three Items
Let’s graph the piecewise perform outlined by:
“`
f(x) = {
x^2, if x < 0
x + 1, if 0 ≤ x < 2
2x – 3, if x ≥ 2
}
“`
To graph this perform in Desmos, we are able to use the next steps:
1. Outline the primary piece of the perform:
“`
f1(x) = piece(x < 0, x^2)
“`
2. Outline the second piece of the perform:
“`
f2(x) = piece(0 ≤ x < 2, x + 1)
“`
3. Outline the third piece of the perform:
“`
f3(x) = piece(x ≥ 2, 2x – 3)
“`
4. Mix the three items of the perform:
“`
f(x) = if(x < 0, f1(x), if(0 ≤ x < 2, f2(x), f3(x)))
“`
5. Graph the perform in Desmos:
“`
y = if(x < 0, x^2, if(0 ≤ x < 2, x + 1, 2x – 3))
“`
The graph of the perform is proven beneath.
[Image of the graph of the function f(x) = {x^2, if x < 0; x + 1, if 0 ≤ x < 2; 2x – 3, if x ≥ 2}]
Desk of Equival
27. The graph just isn’t steady.
This may occur for just a few causes. First, examine to guarantee that your equations are all outlined on the identical factors. If they don’t seem to be, you will want so as to add parentheses to your equations to guarantee that they’re all evaluated within the right order. For instance, the equation
y = |x| + 1
just isn’t steady at x = 0 as a result of absolutely the worth perform just isn’t outlined at 0. To repair this, we are able to add parentheses to the equation to make it
y = (|x|) + 1
which is now steady at x = 0.
One more reason why the graph will not be steady is in case you have not outlined the perform in any respect factors. For instance, the equation
y = x^2
just isn’t outlined at x = 0. To repair this, we are able to add a line to the equation to outline the perform at x = 0, akin to
y = x^2 + 0
which is now steady at x = 0.
Lastly, the graph will not be steady in case you have made a mistake in your equation. For instance, the equation
y = |x| + 1
just isn’t the identical because the equation
y = |x| – 1
and the 2 equations will produce completely different graphs. Just remember to have entered the right equation into Desmos.
If you’re nonetheless having hassle getting the graph to be steady, you’ll be able to attempt utilizing the “Piecewise” perform in Desmos. This perform lets you outline completely different equations for various intervals of the x-axis. For instance, the equation
y = Piecewise(x ≤ 0, -x, x > 0, x)
defines the perform as -x for x ≤ 0 and x for x > 0. This perform is steady at x = 0 as a result of the 2 equations have the identical worth at that time.
Here’s a desk summarizing the completely different causes of a discontinuous graph and easy methods to repair them:
| Trigger | Repair |
|---|---|
| Equations aren’t outlined on the identical factors | Add parentheses to equations to make sure right order of analysis |
| Operate just isn’t outlined in any respect factors | Add strains to equations to outline perform in any respect factors |
| Mistake in equation | Examine equation for errors and proper errors |
| Use of “Piecewise” perform | Outline completely different equations for various intervals of the x-axis |
Optimizing Graph Efficiency
To make sure optimum efficiency when graphing piecewise features on Desmos, take into account the next ideas:
How To Graph Piecewise Features On Desmos
Piecewise features are features which are outlined by completely different expressions over completely different intervals of the enter. They are often graphed on Desmos utilizing the “outline” perform. For instance, the next piecewise perform is outlined for x < 0, x = 0, and x > 0:
“`
f(x) = { x + 1, if x < 0; 0, if x = 0; x – 1, if x > 0 }
“`
To graph this perform on Desmos, you’ll enter the next into the enter area:
“`
f(x) = outline(
if(x < 0, x + 1,
if(x = 0, 0,
x – 1
)
)
)
“`
This may produce a graph of the piecewise perform. The graph could have three segments: one for every of the three intervals of the enter.
Folks Additionally Ask About
What’s a piecewise perform?
A piecewise perform is a perform that’s outlined by completely different expressions over completely different intervals of the enter.
How do I graph a piecewise perform on Desmos?
To graph a piecewise perform on Desmos, you employ the “outline” perform. You will discover extra details about graphing piecewise features on Desmos within the article above.
What are the various kinds of piecewise features?
There are numerous various kinds of piecewise features. Some widespread varieties embrace:
