4.1 Function of several variables

1.

(a) $${D(f) = \{(x,u): xy \geq 0\}, R(f) = [0,\infty)}$$

(b) $${D(f) = \{(x,y): x+y \neq 0\}, R(f) = (-\infty,0) \cup (0,\infty)}$$

(c) $${D(f) = {\mathcal R}^{2} - \{(0,0)\}, R(f) = (0,\infty)}$$ (d) $${D(f) = {\mathcal R}^{2} - \{(0,0)\}, R(f) = [0,1]}$$

(e) $${D(f) = \{(x,y): xy < 1\}, R(f) = (-\infty,\infty)}$$

(f) $${D(f) = \{(x,y,z): x^{2} - y^{2} \neq 0\}, R(f) = (-\infty,\infty)}$$

2.

(a) quadratic cone (b) elliptic paraboloid (c) parabolic cylinder (d) elliptic paraboloid

(e) elliptic cylinder (f) elliptic paraboloid (g) hyperbolic cylinder (h) hyperboloid of one sheet (i) hyperboloid of two sheets