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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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To get the best possible answers, you should explain what your thoughts on the problem are. That way, people won't tell you stuff you already know, and they can write answers at an appropriate level; also, people tend to be more willing to help if you show that you've tried the problem yourself. If this is homework, please add the [homework] tag; people will still help, so don't worry. Lastly, some may consider your post rude because it is phrased as a command, not a request for help, so please consider rewriting it. –  Zev Chonoles Jul 24 '13 at 23:15
    
Thanks Bro,This is my first question on the forum. never knew these small things could hurt some people :) –  Simar Jul 24 '13 at 23:24
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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 $y = |4-|\lfloor x \rfloor| |$? –  Arkamis Jul 24 '13 at 23:25
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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
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@Sigur I used Mathematica's RegionPlot command. –  Antonio Vargas Jul 24 '13 at 23:46

1 Answer 1

up vote 2 down vote accepted

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.

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Yes Got it . Thanks :) –  Simar Jul 24 '13 at 23:38

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