My Math Forum Modules - absolute value HELP

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 February 20th, 2012, 07:12 AM #1 Newbie   Joined: Feb 2012 Posts: 2 Thanks: 0 Modules - absolute value HELP nacrtaj skup svih to?aka T(x,y) ravnine kojima koordinate ispunjavaju uvijet: (|x|-1)(|y|-1)>=0 Draw a set of all points T(x,y) with condition: (|x|-1)(|y|-1)>=0 I don't know how to calculate that problem and I need help.
February 20th, 2012, 08:56 AM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

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Re: Modules - absolute value HELP

Hello, Brunoo1601!

Quote:
 $\text{Draw the set of all points }P(x,y)\text{ with condition: }\:(|x|\,-\,1)(|y|\,-\,1) \:\ge\:0$

$\text{It says: "The product of two quantities is positive (or zero)."}$

$\text{Then: }\:\begin{Bmatrix}\text{(1) the two factors are }\ge\,0 \\ \\ \text{or} \\ \\ \text{(2) the two factors are }\le\,0 \end{Bmatrix}$

$(1)\;\begin{Bmatrix}|x|\,-\,1 \:\ge\:1 &\;\;& \Rightarrow &\;\;& |x| \:\ge\:1 &\;\;& \Rightarrow &\;\;& x\,\le\,-1\text{ or }x\,\ge\,1 \\ \\ \\
|y|\,-\,1\:\ge\:1 && \Rightarrow && |y|\:\ge\:1 && \Rightarrow && y\,\le\,-1\text{ or }y\,\ge\,1 \end{Bmatrix}$

$\text{The graph looks like this.}$

Code:
       ::::::   |   ::::::
::::::   |   ::::::
::::::   |   ::::::
- - - + - + - + - - -
:   |   :
--------+---+---+-------
:   |   :
- - - + - + - + - - -
::::::   |   ::::::
::::::   |   ::::::
::::::   |   ::::::
$(2)\;\begin{Bmatrix}|x|\,-\,1 \:\le\:1 &\;\;& \Rightarrow &\;\;& |x| \:\le\:1 &\;\;& \Rightarrow &\;\;& -1 \,\le\, x\,\le\,1 \\ \\ \\
|y|\,-\,1\:\le\:1 && \Rightarrow && |y|\:\le\:1 && \Rightarrow && -1\,\le\,y\,\le\,1 \end{Bmatrix}$

$\text{The graph looks like this.}$

Code:
            :   |   :
:   |   :
- - + - + - + - -
::::|::::
------::::+::::------
::::|::::
- - + - + - + - -
:   |   :
:   |   :
|

Therefore, this is the graph of the function:

Code:
       :::::*   |   *:::::
:::::*   |   *:::::
:::::*   |   *:::::
* * * *.*.*.*.* * * *
*:::|:::*
--------+:::+:::+------------
*:::|:::*
* * * * * + * * * * *
:::::*   |   *:::::
:::::*   |   *:::::
:::::*   |   *:::::

 February 20th, 2012, 09:34 AM #3 Newbie   Joined: Feb 2012 Posts: 2 Thanks: 0 Re: Modules - absolute value HELP thanks

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