Domain and Range Restrictions

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 {}. For example, y=2x{1<x<3} would graph the line y=2x 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.

 

 
 
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32 Comments

  • -1
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    Daniel S

    Please help. My function is y<2x+1 {-1<x<0} {-1<y<1}
    It should appear as a triangle, but instead says that one side of the inequality must be a polynomial. I only have this problem when restricting domain AND range. How can I fix this?

  • -1
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    Team Desmos

    Hi Daniel,

    Try a double-sided inequality, like this: https://www.desmos.com/calculator/g9c25jolzl

    If you have any other questions, let us know in the feedback box in the calculator.

    Happy graphing,

    Jenny + Team Desmos

  • -2
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    Boone

    Is there any way to remove all of my restrictions at once?

  • 0
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    Dario Chaiquin

    How do you state multiple restrictions in one set of curly brackets?

  • 0
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    Mokdad Mokdad

    Hi,
    I'd like to plot a domain indexed by a parameter k that takes values -2,-1,0,1,2 , all at the sametime. For example I want to draw the squares k<x<k+1 {k<y<k+1} for all values of k at the sametime so I would have 5 squares on the graph. How can I do that without explicitly stating the five domains in separate lines.
    Thanks

  • -1
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    Blake Barto (Rain)

    Can you limit a polar equation? say, for example, I want the following: r=.9^-θ   to stop at a certain point, and not spiral on forever. How can I do that?

    Edited by Blake Barto (Rain)
  • -1
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    Team Desmos

    Blake - try using "theta" in your restriction like {0<theta<pi}.

  • -1
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    Ahedman

    Does desmos limit the domain? When I graph the function r\ =\ \sin \left(\frac{3\theta }{8}\right)\left\{0<\theta <12\pi \right\}, I see no changes to the graph when increasing the upper bound of the domain. I would like to plot this function over a larger domain than [0,12pi]. 

     

  • -1
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    Team Desmos

    Ahedman - Polar graphs are automatically set to a domain of [0, 12pi]. It's possible to restrict the domain to a smaller interval but not to make it larger. 

  • -1
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    Ahedman

    That is a supremely unfortunate.I strongly recommend that you increase both the upper and lower bound in future versions. There are a number of interesting functions I would like to show my students that your program is now useless for. 

  • 0
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    Carolina Kettles

    My equation is y=(4.4)/(x-0.34)+4000 and I'm trying to set the domain so that I have a line segment between y=6.6 and y=32.14 (using a linear equation would be much easier, but I need to use this equation for a project). When I try to set the domain it seems that I can only make it so that y>6.6 but not y<32.14 at the same time without the graph disappearing. Is there any way for me to set the domain to fulfill those requirements?

  • 3
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    Vicente Jiménez

    Hi,

    No problem with the use of restrictions in the domain or range, but how do you type "not equal?

  • -1
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    Shinji

    Hello,

     

    I have trouble to understand what does it mean restrictions in Calculus: Integral with adjustable bounds sheet (https://www.desmos.com/calculator/u2qz73ufju)

    we can find this  0<=y<=f(x) {(a-x)(b-x)<0}

     

    I don't understand this restriction {(a-x)(b-x)<0}

     

    can you help me please ?

     

    best regards

     

  • 1
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    8365494

    How do you put a range restriction that includes an "or"?

  • 1
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    Isaac Parlin

    I have the same question as 8365494. How can you add an "or" to your restriction?

    For example, is there any way I could create a line, and then effectively erase intermittent segments of it by adding multiple domain restrictions using "or"?

  • 0
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    Stryde - (Ari Stryde)

    Is it possible to remove 1/4 of a circle?

  • 0
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    Ryan Walden

    I would like to use mod in the domain of my equation.

    ie.

    f(x)=x+1 {mod(x,3)=0, 0<x<=6}

    the graph should have the following outputs

    (3,4) (6,7) 

    instead I get a graph for f(x)=x+1 {0<x<=6}

    can I not use mod in my domain or is this a syntax error on my part?

  • 0
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    Ahedman

    Ryan, 

    For some reason the desmos engine doesn't do mod(x,3)=0, perhaps it's graphing an "infinately" small point. If you allow the value of the modular function to be less than a small number, say, mod(x,3)<0.01, then you will see the points you expect. As for the second restriction, commas are interpreted as "or", so desmos is graphing values that the mod is zero OR x is between 0 and 6. To use an "and", you need to use a pair of brackets for each restriction. The fucntion below should give you what you're looking for.  

    f(x)=\left(x+1\right)\left\{\operatorname{mod}(x,3)<0.01\right\}\left\{0<x<6\right\}

    Edited by Ahedman
  • -1
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    Thecht319

    I tried to limit the range (r value) on a polar equation inequality, but it wouldn't let me. It said polar equations must be linear in r. I don't see why r can't be limited under these conditions, is this just something Desmos doesn't let you do?

  • -1
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    Jonathandavis

    Could you please implement not equal inequalities in the future. It would help a lot.

  • 2
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    Adam Hrankowski

    Can I restrict the domain to integers?

  • -1
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    Bnichols

    I second Adam's request about restricting the domain to integers.

  • -1
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    1chanian

    Can you check my circle, at kirby's legs, there is still some lingering lines after stating the restrictions.

    https://www.desmos.com/calculator/a8edw3bdpi

    Thanks

  • -1
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    The Harcore Nodder

    Is there a "when....then" kind of restriction?

    How would you make it so that if you split a circle into four, three parts remain and the fourth doesn't?

  • -1
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    Atulac1

    How do you limit a parabola?

  • -1
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    jman23bball

    I made this rough animation of pacman using domain and range restrictions.

    https://www.desmos.com/calculator/28ykwdijnt

     Press play on m to make his mouth move and slide the black dot below him to move pacman.

  • -1
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    Eytan Melamud

    Hi. I tried to limit domain and range. Fine with {-10<x<10} but when adding {-10<y<10} it gives me a nested too deeply error. The annoying thing is it worked for about 10 seconds before deciding it didn't like it. Also any ideas on limiting lines to within the bounding circle would be much appreciated :-)

    Thank you  

    https://www.desmos.com/calculator/gxvswfp621

     

  • -1
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    Nadia Olea

    How can you do the parent function into domain and range in desmos?

     

  • 0
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    Candace

    Hey! 

    I currently have no idea how to add a table onto an equation? I use Desmos all the time, and I'm having trouble with this. 

    This is what happens when I try to add a table onto an inequality. It doesn't give me the option to, and I still can't figure it out.

    I need the points on a table to be able to understand this more, but I'm restrained to otherwise.

    If anyone knows how to add a table onto an inequality like this, that'd be great. 

  • 1
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    Velascri

    I have an assignment in my algebra class to create a picture on a graph with desmos - I'm trying to make a panda and am having trouble making the ears because I want the circles for the ears to be jutting out from the head rather than connected to it at one point. With this, I have to adjust the domain and range of the ear circles to exclude the part of it that is inside the head circle. How do I do this?

     

    The equations for the circles are as follows

     

    Head circle - x^2 + 1.5y^2 = 100

     

    Ear circles - (x + 8)^2 + (x - 5)^2 < 15, (x - 8)^2 + (x - 5)^2 < 15 (it's supposed to be less than or equal to, I just don't know how to type that)

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