How to plot this region in (x,y) space

[maverick280857]

Hi everyone

I need some help with an elementary problem...I have to sketch the region described by

[tex]max(|x|,|y|) \leq 1[/itex]<br /> <br /> I know what max and mod (absolute value) mean but I'm just troubled because of the occurrence of $|y|$. Any help would be appreciated...<br /> <br /> PS--This is <b>not</b> homework.<br /> <br /> Thanks and cheers<br /> Vivek[/tex]

 

[kleinwolf]

This is just the desciption of the square of 2unit side length, centered in (0,0). Usually in that kind of formalism, (x,y) are describing the coordinates of a point on a "ideally" flat infinite plane...In your case you just take all points for which -1<=x,y<=1 which is separated into -1<=x<=1 and -1<=y<=1, because there is no relationships between x and y given here.

 

[maverick280857]

Thanks.

The thing is..how do you reconcile with the occurrence of $|y|$?? I mean...how are you to compare the two operands? Are x and y independent variables in the two orthogonal directions?

I know that

$$max(x,y) = \frac{x+y}{2} + |\frac{x-y}{2}|$$

Does this fit in somewhere?

 

[kleinwolf]

Yes, x and y are independent...you just compare as the max functions say : max(x,y)=x if x>y and max(x,y)=y if y>x...you could do : max(|x|,|y|)<=1 equiv. to |max(x,y)|<=1 and with your formula : $$\frac{1}{2}|x+y+|x-y||<=1$$

 

[maverick280857]

I'm sorry I'm somewhat dumb...I can't see how I can plot the max of two independently varying numbers...some more spoonfeeding needed.

 

[HallsofIvy]

If |x|< |y| then max(|x|,|y|)= |y|. Graph |y|= 1.
If |y|< |x| then max(|x|,|y|)= |x|. Graph |x|= 1.

Those two graphs form the boundary of the region. Now do you see what the region is?

 

[maverick280857]

Great. Thanks! I see it now

I realize how dumb I've been throughout this thread!

Anyway thanks for all your help.

Cheers
Vivek