Vertical Sections and Level Curves

[Juggler123]

I need to find the vertical sections and level curves of the function z=max(x,y^{2}) associated with the constants 1,2,3 and 4.

I know that the function defined in this way basically means that f(x,y)=x if x\geqy^{2} or f(x,y)=y^{2} if x\precy^{2}

But I don't know where to go from here, I've been able to sketch lots of vertical sections and level curves for 'normal' functions but this is just confusing me. Can anyone help please? Thanks.

 

[LCKurtz]

Here's a picture of it that may help you visualize it: