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.

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 $y$.
