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 pairs $$(x,y)$$ such that $$x + y > 0$$. 4. This inequality can be rewritten as $$y > -x$$. 5. The domain is the half-plane above the line $$y = -x$$, not including the line itself because $$\ln(0)$$ is undefined. 6. To graph the domain, draw the line $$y = -x$$ and shade the region above it. 7. The boundary line $$y = -x$$ is dashed to indicate it is not included in the domain. Final answer: The domain of $$f(x,y) = \ln(x + y)$$ is $$\{(x,y) \in \mathbb{R}^2 : y > -x\}$$.