# 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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• Daniel S

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?

• 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

• Boone

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

• Dario Chaiquin

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

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

• 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)
• Team Desmos

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

• 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].

• 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.

• 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.

• 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?

• Vicente Jiménez

Hi,

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

• 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

• 8365494

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

• 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"?

• Stryde - (Ari Stryde)

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

• 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?

• 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
• 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?

• Jonathandavis

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

Can I restrict the domain to integers?

• Bnichols

• 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

• 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?

• Atulac1

How do you limit a parabola?