1. ## Partial Derivatives.

I need help understanding these questions. This is new and my teacher just went over this stuff but I'm still having some trouble...

f(x,y) = y - x

Find
Domain
Range
Level curves Is this also called contour curve?
Boundary of the functions domain
Determine if open region, closed or neither.
Decide if the domain is bounded or unbounded.

Need help with the bolds! Please explain too!

2. Hello

Originally Posted by aeubz
I need help understanding these questions. This is new and my teacher just went over this stuff but I'm still having some trouble...

f(x,y) = y - x

Find
Domain
This function would be considered a plane. It is continuous everywhere, so it would exist $\forall~x\in\mathbb{R}$

Range
The same idea applies here as well. It would also exist $\forall~y\in\mathbb{R}$

Level curves Is this also called contour curve?
Level curves and contour curves are the same. Let $z=k$. We see then that the cross section of this plane and the plane $z=k$ will have the form of $k=y-x\implies y=x+k$. Thus, the contour lines will be linear, and as k varies (positive or negative), the contour lines vary.

Here is the contour plot:

Boundary of the functions domain
Hmm...I would say that the boundary of the domain would be $(-\infty,\infty)$, but if anyone one else wants to chip in something, that would be great

Determine if open region, closed or neither.
Could you try to elaborate a little bit more on this?

Decide if the domain is bounded or unbounded.

Need help with the bolds! Please explain too!
Since the domain approaches both positive and negative infinity, the domain would be unbounded [someone correct me if I'm wrong]