# How to draw the graphs for these functions?

Could I please be helped with the graphs for the following functions:

$$y=\lceil \tan x \rceil, \quad y=\tan (\lceil x \rceil), \quad y=\lceil \tan (\lceil x \rceil) \rceil$$

I have been able to form the graphs for the sine and cosine functions based on the fundamentals of the greatest integer function. However I am having problems with $\tan$ and $\cot$ graphs.

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What do square parens mean? – Kaster Jul 5 '14 at 7:00
@fantini, it's still the same, pls use \lceil \rceil – Vikram Jul 5 '14 at 7:11
I've changed to ceiling then, adding parentheses to avoid confusion. – Mark Fantini Jul 5 '14 at 7:13
What do you mean 'How to draw the graphs'? – harogaston Jul 5 '14 at 7:19
Yeah, I know they still remain the same... could I please be helped with their graphs? I mean where should the original graphs be modified so that get these movements! – Shamayeta Jul 5 '14 at 7:19

Start with a graph of $\tan x$. For $\lceil\tan x\rceil$, mark all points of $\tan x$ where the $y$ coordinate is integer. The graph of $\lceil\tan x\rceil$ is a staircase with these points as right ends (because $\tan$ is monotonically increasing ).
For $\tan\lceil x\rceil$, mark th epoints in $\tan x$ with integer $x$ coordinate instead. Again, thes points mark the right ends of the staorcase steps (even across the poles).
For $\bigl\lceil \tan\lceil x\rceil\bigr\rceil$, start with the previous graph and move the steps up to the next integer $y$.