# graphing inequalities

• May 21st 2008, 08:14 PM
jmmsan
graphing inequalities
how do you graph xy<12?
i can't find any examples in my book :(.
thank you!
• May 21st 2008, 08:29 PM
xy<12
I suppose you could do this:
Transform xy<12 to y<12/x.
Sketch the graph y = 12/x, a hyperbola if I am correct.
Change your curves to dotted boundaries.
Select some test points to find regions where xy<12.
Shade the areas for which xy<12.

I think you will have a two-dimensional graph at the end.

Bye.
• May 21st 2008, 08:32 PM
TheEmptySet
Quote:

Originally Posted by jmmsan
how do you graph xy<12?
i can't find any examples in my book :(.
thank you!

Isolate y in the inequality to get

$\displaystyle y < \frac{12}{x}$

Now we want to graph $\displaystyle y=\frac{12}{x}$

This hyperbola divides the xp plane into 3 parts. We need to check a values from each one to find where to shade.

when we check the origin (0,0) in the orginial we get $\displaystyle 0 \cdot 0 \le 12$ This is true

So we shade the part inbetween the two hyperbola's see the attached graph.

Good luck.

Attachment 6439