# Function Tables

Columns of tables in Desmos.com have different behavior depending their headings. If you put an function of x in the 2nd header we'll fill it in as a function table, calculating the values for you.

For example, if you have "x_1" and "2x_1+1" as your headings, we'll fill in the 2nd column for any point you put in the first: Note that you can write rich math expressions in the cells, including things like pi/2: To compare two functions side by side, add another column and enter another function into the new heading: Note that you can convert any graphed function into a function table, by pressing the "edit" button, and then the "generate table" option for that function:

Step 1: Step 2: If you'd like to learn more about tables, check out the Tables page at Learn Desmos:

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#### 21 Comments

• esolanda

Really usefull, thanks :)

• Katie Coleman

thank you!!! XD

• Joseph Shelton

Is there a way to do this the other way around? i.e. Create a function from a set of data.

• mlane (dusky)

Umm so what are the limits of tables? How big can a table be? Do you think I could plot about 1523 to 4857 planets err.... I mean data points using desmos? What would be the best way to pull in large set of data?

Also can function tables be defined abstractly/indirectly? For example instead of the directly making a table sin(x), Making a table f(x), then define f(x) = sin(x)? This would be really useful to know for functions that have very long terms such as
f(x) = sqrt(1 - (cos(27.13/180*pi)*sin(pi*t)-sin(27.13/180*pi)sin(x-192.85/180*pi)cos(pi*t))
where -pi/2 < t < pi/2

• mlane (dusky)

Could you have a table of notes? or things "" for each element?

• Abotting213

I have two functions which I've written out and graphed in Desmos: w=f(x) and s = g(x). Now, I want a cross plot such as in a table with heading f(x) and g(x), but it won't seem to let me do that. I believe this might be called a "parametric" graph so I can see the behavior of w as it relates to s for the same parameter, x.

• Natasha Hansen

I want to enter a table and have it give me the function rule. Can I do that?

• Leonardo Cisija

For anyone on here looking for a way to make it "do the reverse" and give you a rule, regression is the key.

Basically, you take the header of the output column you want (lets say M) and write a generic looking equation using just letters. Use the tilde symbol instead of equals. For example:

M ~ mx + b

This will make Desmos give you values for m and b that fit the data best, as well as give you the R^2 value which tells you how closely it fits (1 is best). Does it have to be linear? Nope. you can certainly find a line of best fit for a curvy set, but it can work with polynomial expressions too. Desmos warns that the regression is only really effective with linear and polynomial functions (including parabolas, cubics, conic sections, etc.), but I've made it figure out some pretty freaky ones. here are some examples from Desmos:

Linear:
https://www.desmos.com/calculator/jwquvmikhr
Line of best fit (and other cool stuff):
https://www.desmos.com/calculator/paknt6oneh
Polynomial:
https://www.desmos.com/calculator/sanlujpfmc

This one has 4 graphs from something I was working on:
https://www.desmos.com/calculator/ejoqasul6s
(note, it uses w instead of x)

The "log mode" is just a different algorithm that usually gives you the same thing but might save your life if the graph is being weird.

Edited by Leonardo Cisija
• Pxt2658

Is is possible to generate a table with a start value (such as 0, an an increment such as 0.001?

• Leonardo Cisija

This is just off the top of my head, but you can make a set using a linear equation and then tell Desmos to fill out a table for it.

Y = m[0...x] + b

where Y is the name of the set, m is the increment, x is the number of items, and b is the start value.

Then, you put Y (or whatever you name the set) in the table, and it will fill out the column for you. I did yours as an example in the picture. Actually, now that I think about it, you can just enter the expression right in the column header instead of making a set.

Edited by Leonardo Cisija
• Pxt2658

Cool that you can use a list in an expression. Thx.

• Tbower

How can I fill the abscissa (first) column? • Leonardo Cisija

You can't directly, but you can very easily have Desmos define an equivalent set. The downside is the table will not reflect changes to the x-set unless they're done directly to the table, but you can easily just define the table again.

You start by defining your set "b" along with a function or another list. Then you pair them up as you would with coordinates. If you're using a function, make sure it's taking the set as an input. Then hit the options button and click the table symbol that appears over the pair.  Desmos will then turn the pair into a table of 2 new sets that are equivalent to the originals. You can add new functions and sets to the table, including replacing the y-set with the original function or set you wanted.

Edited by Leonardo Cisija
• Oliaksandr Shōwa Tenno Prughović

Soooo it doesn't even give me the option to covert my graphed functions into a table. Please fix. • Leonardo Cisija

Solve it for a variable. The function shown there isn't defined explicitly for either variable ("y=" or "x="), so Desmos has no way of telling input from output or if a table can even be made.

For example, y = 2x + 1 can be converted with x as the input and y as the output. On the other hand, y^2 + x^2 = 1 cannot because neither y nor x have unique outputs.

Edited by Leonardo Cisija
• TheGoldenProof

how can you get the derivative of a table? Edited by TheGoldenProof
• Leonardo Cisija

That looks a lot like world population. The derivative of a line graph is just the slope between any two points, but I assume you mean the derivative of a curve that fits the line graph. In this case, regression is your friend.

First we pick a type of function that fits our data. For population, exponential is best. Now we write an exponential function with y1 and x1 and a bunch of parameters (just random letters). Instead of an equals sign, use a tilde ~

Now, Desmos fills in the parameters with actual numbers. We just write the same exact thing but replace y1 with f(x) and x1 with regular old x.

Finally, just take the derivative. edit: you can also use the notation f'(x) to take the derivative faster (instead of d/dx)

Edited by Leonardo Cisija
• # G1T R3KT BRUH

I have a table all filled in with the rule but I don't know how to enter the rule into the online Desmos Graphing Calculator.

I NEED HELP CHANGING THE RULE

------------------------------------------------------------------------------------------------------------

HERE IS MY CURRENT TABLE AND GRAPH Edited by # G1T R3KT BRUH
• Leonardo Cisija

Are you asking how to put a rule into the table, or how to get Desmos to write a rule based on the points you out in?

If you want to enter a rule into the table, just write a formula on top in terms of x1. For example, x1 + 2. If you want to get Desmos to figure out the rule, you have to use the regression feature. I've explained and provided examples for both here: https://www.desmos.com/calculator/qt9yqcdjmd

HOWEVER, Desmos doesn't support recursive rules, only explicit functions. If your rule looks like this:
Un = 2 * Un-1
Then you have to rewrite it as:
y = 2^x

• skylord a52

It doesn't seem possible to copy from function tables at the moment. Am I just missing something? And if it's not possible, will this be added in the future?

• JACKSON GASCON

9*9=72

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