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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24 Comments

  • 0
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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?

  • 0
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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

  • 0
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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

  • 0
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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)
  • 0
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    Team Desmos

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

  • 0
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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]. 

     

  • 0
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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. 

  • 0
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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. 

  • 1
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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?

  • 2
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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?

  • 0
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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?

  • 1
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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
  • 0
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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?

  • 0
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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?

  • 0
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    Bnichols

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

  • 0
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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

  • 0
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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?

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