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

question 318

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 \(4 x ^ { 2 } + 2 y ^ { 2 } = c\)

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