Quick Question; sketching regions (1 Viewer)

[noobonastick]

Hi, i have a quick question i would like to ask;

"Sketch the region defined by the inequality"

y<3/x

and

x<4/y

I was just wondering, how do you test the points to know where to shade in the regions..?

Thanks for your help =]

 

[DownInFlames]

a) draw the graph for y = 3/x

use xy = 3 if it's easier for you: plot (1,3) (1.5,2) (3,1) and the negative sides (-1,-3) etc. and draw in the curves.

it's a hyperbola.

the shaded region is where the y value is less that 3/ x value, so basically under the line... I'm drawing a picture in paint that I'll put in in a moment...

 

[DownInFlames]

Here's the picture:

quadrant 1: Substitute (1,1) to find that you need to shade under the line
quadrant 2: y will always be positive, 3/x will always be negative so you don't shade here.
quadrant 3: substitute (-1,-1) to find that you don't shade above the line, substitute (-3,-3) to find that you do shade below the line.
quadrant 4: y will always be negative, x will always be positive, so shade the whole thing.

 

[tacogym27101990]

except the line needs to be dotted
as its less than
but that would be really hard to do on paint

 

[DownInFlames]

except the line needs to be dotted
as its less than
but that would be really hard to do on paint

picky picky. You're right though. I didn't actually think of that.

 

[noobonastick]

haha thanks, I already knew it was a hyperbole and how to plot it (lol simple).

So basically i have to test every quadrant. Thanks

 

[DownInFlames]

haha thanks, I already knew it was a hyperbole and how to plot it (lol simple).

So basically i have to test every quadrant. Thanks

yeah that's about it. It only takes about 5 seconds to think each part through...