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.
Verbatim is defined as an exact repetition without changing the words. An example of verbatim is when you quote someone exactly without changing anything. word for word; in exactly the same words. Origin of verbatim.
1 Word for word; in exactly the same words as were used originally.  I have copied his speech and here it is, verbatim. ( 1 of a document) Corresponding with the original word for word. ( of a person) Able to take down a speech word for word, especially in shorthand.