Question

How would you graph the function f(x)= [[x]]+[[-x]]

Answer 1

this has something to do with greatest integer?

Answer 2

Yes. It's a greatest integer function

Answer 3

This works similar to the ceiling function.
\[f(x)=[[x]]+[[-x]] = \lceil x \rceil + \lceil -x \rceil = \lceil x \rceil - \lfloor x \rfloor\]
The function is equal to 1 at all non-integer points, equal to 0 at integer points.
So,
\[f(x)= 1 \text{ when } x \notin \mathbb{N} , 0 \text{ when } x \in \mathbb{N}\]
See the attached graph.