Answer
Domain: x, y can be any real numbers in the x-y plane.
Range: $f(x,y) \gt 0$
Level Curves: $x+y = \ln{c}$ (constant),
Work Step by Step
Function: $f(x,y) = e^{x+y}$
Domain: x, y can be any real numbers in the x-y plane.
Range: $f(x,y) \gt 0$
Level Curves: $f(x,y) = c$ (constant),
$e^{x+y}=c$
$\ln{e^{x+y}}=\ln{c}$
$x+y = \ln{c}$ (constant)
Hence, the level curves are a series of straight lines.
For example, when $c=e$,
$x+y = 1$ which is shown in the figure.
