Find the Domain and Range and Describe the Level Curves $$f ( x , y ) = 4 x ^ { 2 } - 2 y ^ { 2 }$$

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
- $$f ( x , y ) = 4 x ^ { 2 } - 2 y ^ { 2 }$$

A) Domain: all points in the first quadrant of the $x y$ -plane; range: all real numbers; level curves: hyperbolas $4 x ^ { 2 } - 2 y ^ { 2 } = c$
B) Domain: all points in the $x y$ -plane; range: all real numbers; level curves: hyperbolas $4 x ^ { 2 } - 2 y ^ { 2 } = c$
C) Domain: all points in the $x y$ -plane; range: real numbers $\mathrm { z } \geq 0$ ; level curves: ellipses $4 x ^ { 2 } + 2 y ^ { 2 } = c$
D) Domain: all points in the xy-plane; range: all real numbers; level curves: ellipses $4 x ^ { 2 } + 2 y ^ { 2 } = c$