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

---

Definitions:

Bouquets

An arrangement of flowers that are typically gathered at the stems and often used as gifts or decorations.

Variable Costs

Costs that change in proportion to the level of output or activity in a business.

Square Feet

A measure of area in the imperial system, used to calculate the size of a space, equivalent to the area of a square with sides one foot in length.

Variable Costs

Costs that vary directly with the level of production or output.