Relate a function's domain to its equation, graph, and context, especially when model choice matters.
Separate mathematical and contextual domains
Problem
For \(A(x)~=~\sqrt{x~+~4}\) with \(x\) a physical side length, state the mathematical domain and exclusions, the contextual domain and input type, the context-only exclusions, and the relationship between the domains.
Big Picture
What this problem is really about
Keep two domain questions on separate lines. First let the square-root formula determine its full algebraic input set; then classify the side length as a continuous physical measure and impose strict positivity. Comparing the sets afterward reveals which inputs fail only because of context and whether the physical domain is equal to or properly contained in the mathematical one.
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