Trouble Graphing Multivariable Functions

[_Steve_]

So the function I'm working with is:

f(x,y) = 1/sqrt(1-x^2-4y^2)

First, they want me to find the Domain and Range, which I found to be:
D: x^2 + 4y^2 < 1
R: (0,1]
Then they want me to sketch level curves and cross sections, then sketch f(x,y)
I'm having trouble with the sketching, I understand the concept of level curves, but when I make f(x,y) = k I'm not quite sure where to go from here... Does anyone have any graphing tips that I could use? Thanks!

 

[maysenator]

i wouldn't mind some insight on this as well.

 

[SammyS]

You know that 0 ≤ x² + 4y² because x² & y² are each non-negative.

∴ 0 ≤ x² + 4y² > 1

So to find level curves, you must choose k so that 0 ≤ 1/k ≤ 1 .