Need help with level curves

Hello everyone!(Hi)

Well,I'm having a problem drawing level curves for piecewise functions.

The problem is, how do I know which value the constant **k** will hold?

The function is the following:

$\displaystyle f(x,y)=: $

$\displaystyle 4$ **if ** $\displaystyle x^2+y^2<=16$

$\displaystyle sqrt(32-x^2-y^2 )$ **if** $\displaystyle 16<x^2+y^2<=32$

The solution I've attempted and which I'm not sure it's correct is:

I've drawn a level curve of level 4,because it's within the domain of f(x,y)(which is $\displaystyle ]-infinity;32]$) and it's the point where the function changes to the other branch.

Does this make sense?

Just another question,to determine the domain of the second "piece" of the function,why do we also use the sqrt(32-x^2-y^2) condition and not only just the **if** clause?

Thanks in advance for the reply!