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 constant 1,2,3,4 so that I can sketch them.

I know given z=f(x,y) then the vertical sections of the function are z=f(c,y) where c is a constant and the level curves are c=f(x,y). I've been able to sketch other problems similar to this but I don't understand the function z=max(x,y^2). Can someone help please?

Thanks!

 

[LumenPlacidum]

I recommend first solving where x > y^2. z = max( x, y^2 ) means z is whichever value is greater at any given (x,y) input.