Okay can anyone explain the graph of function $$\lfloor|y|\rfloor = 4 -\lfloor|x|\rfloor$$ where $|\cdot|$ denotes Absolute Value Function and $\lfloor\cdot\rfloor$ denotes the floor function (Greatest Integer Function).
This is an interesting function as i was told by my teacher that this graph actually corresponds to an area. I could atmost plot |y|=4-|x|
Hint:
Notice that for $-1<x<1$, we have $\lfloor|x|\rfloor$=0, so the corresponding $y$-values must satisfy $\lfloor|y|\rfloor=4$. This means $-5<y\le-4$ or $4\le y<5$. This portion of the graph corresponds to two rectangles. Can you see them?
Now, see if you can continue for the domains $\{-2<x\le-1$ or $1\le x<2\}$, $\{-3<x\le -2$ or $2\le x<3\}$, and so on.