If z is a function of two variables given by
z = (x² + y²)^0.5 - 1

i) Find the domain & range of the function
ii) Sketch the surface of the function
iii) Sketch the level curves of the function for z= -1, 0, 2

Question

If  z is a function of two variables given by 
z =  (x² + y²)^0.5 - 1

i) Find the domain & range of the function
ii) Sketch the surface of the function
iii) Sketch the level curves of the function for z= -1, 0, 2

anonymous · Answer

The domain should be all real values of x and y: (-inf,inf).
The range should be: [-1,inf) because the smallest possible value of the square root is 0. Ergo, the smallest value of z is -1.

I can't sketch the surface on here or the level curves.