# 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:

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• 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-192.85/180pi)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'll take polynomial expressions too. desmos warns that the regression is only really effective with linear and polynomial (including parabolas, cubics, conic section, etc.) functions, 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)

"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.

• 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.

• Pxt2658

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