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 $5 x + 4 y = c$

Question

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 $5 x + 4 y = c$

Quizplus · Accepted Answer

The logarithm function requires its argument to be greater than zero, hence $5x + 4y > 0$. The range of the logarithm function is all real numbers. Level curves are defined by setting $f(x, y)$ to a constant, resulting in lines $5x + 4y = c$.

Find the Domain and Range and Describe the Level Curves xyx yxy

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