1. The problem statement, all variables and given/known data Find the domain of the function f(x,y) = 1/sqrt(x^2-y). Sketch the level curves f=1, f=1/2, f=1/3. 2. Relevant equations 3. The attempt at a solution Domain is rather simple to find: x^2>y AND x^2-y cannot equal 0. Level curves are also simple to find. They are simply parabolas that are shifted down according to what f =1. For f=1 shift the parabola down 1. For f=1/2 shift the parabola down 4. For f=3 shift the parabola down 9. My simple question is this: Upon looking at my level curve graph, I notice that anything inside the y=x^2-1 parabola is NOT consistent with the domain. I would then 'mark' this section off in my level curve? (say, darken it out and clarify that it is NOT in the domain). or Would I leave it as is as it isn't needed in the level curve? I can't seem to find a clear quick answer on google. Seems logical that I would clarify that it is not part of the graph.