Consider the function (x, y) = x + y. (a) Sketch the graph of the surface given

Consider the function ƒ(x, y) = x² + y².

(a) Sketch the graph of the surface given by ƒ.

(b) Make a conjecture about the relationship between the graphs of ƒ and g(x, y) = ƒ(x, y) + 2. Explain your reasoning.

(c) Make a conjecture about the relationship between the graphs of ƒ and g(x, y) = ƒ(x, y - 2). Explain your reasoning.

(d) On the surface in part (a), sketch the graphs of z = ƒ(1, y)
and z = ƒ(x, 1).