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

question 371

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
-f(x, y) = ln (5x + 4y)

• A) Domain: all points in the \(x y\)-plane; range: all real numbers; level curves: lines \(5 x + 4 y = c\)
• B) Domain: all points in the xy-plane satisfying \(5 x + 4 y \geq 0\); range: all real numbers; level curves: lines \(5 x + 4 y = c\)
• C) Domain: all points in the \(x y\)-plane satisfying \(5 x + 4 y > 0\); range: all real numbers; level curves: lines \(5 x + 4 y = c\)
• D) Domain: all points in the \(x y\)-plane satisfying \(5 x + 4 y > 0\); range: real numbers \(z \geq 0\); level curves: lines \(5 x + 4 y = c\)

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Definitions:

Placenta

An organ that develops in the uterus during pregnancy, providing oxygen and nutrients to the growing baby and removing waste products.

Labor

The process of working or the effort expended on a particular task; also refers to childbirth process.

Allele

A variant form of a gene that arises due to mutation and can be found at a specific place on a chromosome.

Gene

A basic unit of heredity in a living organism that is made up of DNA and positioned on a chromosome; genes contain the information needed to build and maintain an organism's cells and pass traits to offspring.