# Graphing a difficult function

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|

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The function, as you've written it, doesn't make a whole lot of sense. Let's take $x = 40$. Then, $4-\lfloor | x | \rfloor = -36$. But $|y| = -36$ doesn't make sense for any value of $y$. Do you mean $y = |4-|\lfloor x \rfloor| |$? – Emily Jul 24 '13 at 23:25
Yes the range is from [4,-4]. The function only exists within this range. – Simar Jul 24 '13 at 23:32
The set of all points $(x,y)$ satisfying $\lfloor|y|\rfloor = 4 -\lfloor|x|\rfloor$ is not the graph of a function. Here's a plot of this set of points. – Antonio Vargas Jul 24 '13 at 23:36
@AntonioVargas, what program did you use to draw it? – Sigur Jul 24 '13 at 23:39
@Sigur I used Mathematica's RegionPlot command. – Antonio Vargas Jul 24 '13 at 23:46

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.