Sketching regions help!!!

[Sumboody]

Question:

Sketch each of  the following regions:
 e. (x^2 -y^2)<1 and (x^2 plus y^2) <4

how do you work where to shade in? thanks

[pi]

This is a n00b and cheap way. But sub in (0,0) into each equation and if (after subbing) it satisfies the equation, then that is the required region. If sketching both on same axis, do same method (shade later though) but the overlapping required region is the one you want. Remember: a key is needed and both graphs are 'dotted' lines (because of '<'). 

[Andiio]

Just sub in points - that's the most efficient way for all inequalities.

[Sumboody]

 ohh okay i think i got it.
but if it doesnt satify the equation I shade in the outer region?

[pi]

ohh okay i think i got it.
but if it doesnt satify the equation I shade in the outer region?

Its you choice, thats why a key/legend is necessary. If you shaded the un-needed part, than on your legend, who would say that the shaded area is not the required region (or the blank area is the required region).

[Sumboody]

alright thanks

[m@tty]

It is much easier to shade in the unneeded part because then you can work on section at a time and by the end you'll be left with the required region clear instead of having to think about all of the parameters at once. You'd be pushing your luck with the intersection of 4 inequalities if you try and shade only the required region.

[TrueTears]

This is a n00b and cheap way. But sub in (0,0) into each equation and if (after subbing) it satisfies the equation, then that is the required region. If sketching both on same axis, do same method (shade later though) but the overlapping required region is the one you want. Remember: a key is needed and both graphs are 'dotted' lines (because of '<'). 

no not a noob and cheap way it's actually very elegant and intuitive which is great.

however subbing in (0,0) is not always going to work, think about y<x