Calculus 3 help needed. confusing piecewise. I need explanation

[bombz]

Homework Statement

2. On the domain x \geq 0; y \geq 0, dene the function f(x; y) such that

[PLAIN]http://img100.imageshack.us/img100/2144/huhh.jpg

Homework Equations

I'm not so sure.

The Attempt at a Solution

I apologize for no attempt. I am just totally confused with this notation as I have never seen it before. What do I do with this?

 

[tiny-tim]

hi bombz!

I am just totally confused with this notation as I have never seen it before. What do I do with this?

it means that you use the value given (0 1 or -1) for just the area given …

it's a sort of two-dimensional step-function

(and when it says "define the function", that's badly worded, it's not asking you to do something, it means "the function is defined this way" )

 

[bombz]

Dear tiny-tim, how would I use those values then?

So basically,
This isn't a form we are using in class but from the piecewise, I am getting?
f(x,y) = 0 when x+1<y or when y <= x-1

How would I use that to find the domain though?? how would I even sketch it??

Sigh. Any more hints would be greatly appreciated. Part b I figured out with the book. Part a is what my teacher was so cool and added in when he never taught us something like this. I tried asking for help from friends but no one can figure out a.

 

[tiny-tim]

hi bombz!

draw the lines y = x - 1, y = x, and y = x + 1

write the value of f in each region between the lines

(the domain is the whole x,y plane)

 

[bombz]

ahh that makes sense :) thank you so much!