A surface is given by z : f(a3, y) : 71'2 exp (_ yg). (i) Determine the domain and range of f then summarise the answer using set notation. (ii) Find a general equation for the crosssections resulting from the intersection of f with the plane 3; : c, c E R. On the same axes sketch cross-sections for c : 2 to c : 2 in steps of 1 / 2. You may exploit symmetry to simplify this process. (iii) Find a general equation for the cross-sections resulting from the intersection of f with the plane a: : k, k E R. On the same axes sketch cross-sections for k : i2, :1, 0. (iv) Sketch the mesh of the surface using the cross-sections from (ii) and (iii)