# Drawing a graph

• Jun 14th 2013, 06:10 AM
kastamonu
Drawing a graph
How can I draw the graph of |xy| <=0
• Jun 14th 2013, 06:16 AM
Plato
Re: Drawing a graph
Quote:

Originally Posted by kastamonu
How can I draw the graph of |xy| <=0

In order for $\displaystyle |xy|\le 0$ it is necessary for $\displaystyle xy=0$.

Therefore, $\displaystyle x=0\text{ or }y=0$.
• Jun 14th 2013, 07:46 AM
HallsofIvy
Re: Drawing a graph
So the graph is two intersecting straight lines.
• Jun 14th 2013, 09:27 PM
MINOANMAN
Re: Drawing a graph
There is no way to graph this. It is wrong. The | xy| is > =0 for every x,y and not <0
• Jun 15th 2013, 03:39 AM
Plato
Re: Drawing a graph
Quote:

Originally Posted by MINOANMAN
There is no way to graph this. It is wrong.

Why in the world would you post that?

$\displaystyle \{(x,y) : x = 0 \vee y = 0\}$ is the graph in $\displaystyle \mathbb{R}^2$
This is the union of the $\displaystyle x\text{-axis}~\&~y\text{-axis}~.$

$\displaystyle \{(x,y,z) : x = 0 \vee y = 0\}$ is the graph in $\displaystyle \mathbb{R}^3$
This is the union of the $\displaystyle xz\text{-plane}~\&~yz\text{-plane}~.$

There were two correct replies posted. Are you saying that both Prof Halls and I are mistaken?
• Jun 15th 2013, 06:19 AM
MINOANMAN
Re: Drawing a graph
the |x| is never negative as simple as such..........the rest is blabla
• Jun 15th 2013, 06:28 AM
Plato
Re: Drawing a graph
Quote:

Originally Posted by MINOANMAN
the |x| is never negative as simple as such..........the rest is blabla

Do you even the definition of a graph?
• Jun 15th 2013, 07:32 AM
HallsofIvy
Re: Drawing a graph
Quote:

Originally Posted by MINOANMAN
the |x| is never negative as simple as such..........the rest is blabla

You are the one who is "blabla"ing. You seem to have misread the question. The original question was about graphing $\displaystyle |xy|\le 0$, the set of points (x, y) such that xy is either negative or zero. Yes, |xy| is never negative but it is 0. The graph is the two axes- the x- axis on which y= 0 so |xy|= |x(0)|= 0 and the y-axis on which x= 0 so |xy|= |(0)y|= 0.
• Jun 15th 2013, 10:08 AM
MINOANMAN
Re: Drawing a graph
Yes, |xy| is never negative but it is 0.......which implies x=0 and y=0..................I agree.....
do not use the < 0 it is wrong............................................. ......
and be more polite......after all we just exchange here views and ideas....and if we disagree in some issues this is just another expression of the plurality of Mathematics...
• Jun 15th 2013, 10:25 AM
Plato
Re: Drawing a graph
Quote:

Originally Posted by MINOANMAN
do not use the < 0 it is wrong...

Again, why would any mathematically literate person write that?
Now that is being as polite as this situation calls for.

Did you miss read the OP?
The OP was $\displaystyle |xy|\le 0$ not $\displaystyle |xy|<0$.
If it had been the latter, then we all would agree that no nonempty graph exists.
• Jun 16th 2013, 10:58 PM
kastamonu
Re: Drawing a graph
Quote:

Originally Posted by HallsofIvy
So the graph is two intersecting straight lines.

Many Thanks. At first I thought it was the graph of a hyperbolia. But I wasn't sure because of the absolute value sign.