Find the domain and range and describe the level curves for the function f(x,y).
-$$f ( x , y ) = e ^ { x + y }$$
A) Domain: all points in the first quadrant of the xy-plane; range: all real numbers; level curves: lines x + y = c
B) Domain: all points in the xy-plane; range: real numbers z 0; level curves: lines x + y = c
C) Domain: all points in the first quadrant of the xy-plane; range: real numbers z 0; level curves: lines x + y = c
D) Domain: all points in the xy-plane; range: all real numbers; level curves: lines x + y = c

Question

Find the domain and range and describe the level curves for the function f(x,y).
-$$f ( x , y ) = e ^ { x + y }$$
A) Domain: all points in the first quadrant of the xy-plane; range: all real numbers; level curves: lines x + y = c
B) Domain: all points in the xy-plane; range: real numbers z > 0; level curves: lines x + y = c
C) Domain: all points in the first quadrant of the xy-plane; range: real numbers z > 0; level curves: lines x + y = c
D) Domain: all points in the xy-plane; range: all real numbers; level curves: lines x + y = c

Quizplus · Accepted Answer

The function $f(x, y) = e^{x+y}$ is defined for all real numbers $x$ and $y$, so its domain is all points in the xy-plane. The exponential function always yields positive values, so the range is $z > 0$. The level curves are given by setting $f(x, y) = e^{x+y} = c$, where $c$ is a constant, leading to $x + y = \ln(c)$, which are lines in the xy-plane.

Find the Domain and Range and Describe the Level Curves f(x,y)=ex+yf ( x , y ) = e ^ { x + y }f(x,y)=ex+y

Find the Domain and Range and Describe the Level Curves $f ( x , y ) = e ^ { x + y }$