Find the Domain and Range and Describe the Level Curves $x y$

question 32

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
-f(x, y) = -6x + 8y

• A) Domain: all points in the \(x y\)-plane; range: real numbers \(z \geq 0\); level curves: lines \(- 6 x + 8 y = c , c \leq 0\)
• B) Domain: all points in the \(x y\)-plane; range: all real numbers; level curves: lines \(- 6 x + 8 y = c\)
• C) Domain: all points in the \(x y\)-plane; range: all real numbers; level curves: lines \(- 6 x + 8 y = c , c > 0\)
• D) Domain: all points in the \(x y\)-plane; range: real numbers \(z \geq 0\); level curves: lines \(- 6 x + 8 y = c , c \geq 0\)

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Definitions:

Parallel Shift

Parallel shift is a concept in economics where a graph, such as a demand or supply curve, shifts left or right without changing its slope, indicating a uniform change in demand or supply.

Budget Line

A line that shows the different combinations of two products a consumer can purchase with a specific money income, given the products’ prices.

Consumer's Level

Refers to the consumption patterns, preferences, and purchasing power of individuals or households within an economy.