1. The problem asks to determine and graph the domain of the function $$f(x,y) = \ln(x + y)$$. 2. The natural logarithm function $$\ln(z)$$ is defined only for $$z > 0$$. 3. Therefore, the domain of $$f(x,y)$$ is all points $$(x,y)$$ such that $$x + y > 0$$. 4. The boundary of the domain is the line where $$x + y = 0$$. 5. To graph the domain, draw the line $$x + y = 0$$, which can be rewritten as $$y = -x$$. 6. The valid domain is the half-plane above this line where $$x + y > 0$$. 7. This means all points above the line $$y = -x$$ are included in the domain. Final answer: The domain of $$f(x,y) = \ln(x + y)$$ is $$\{(x,y) \in \mathbb{R}^2 : x + y > 0\}$$, the half-plane above the line $$y = -x$$.