Problem

For \(A(x)~=~8~+~500/x\), where \(x\) is a positive whole number of items and \(A\) is average cost in dollars per item, find the algebraic intercepts, check their feasibility, and interpret the contextual result.

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Algebra: x-intercept (−62.5,0); no y-intercept because x=0 is undefined. Feasibility: −62.5 and 0 are outside the positive-whole-number domain. Interpretation: neither intercept is contextual.

Algebra: no x-intercept because average cost stays positive on the domain; y-intercept (0,8). Feasibility: positive item counts are allowed, but 0 is excluded. Interpretation: the claimed y-intercept is not contextual.

Algebra: x-intercept (62.5,0); no y-intercept because x=0 is undefined. Feasibility: 62.5 is positive but not a whole number, and 0 is excluded. Interpretation: neither intercept is contextual.

Algebra: x-intercept (−62.5,0); y-intercept (0,8). Feasibility: −62.5 is outside the domain, but 0 is claimed feasible. Interpretation: only the claimed y-intercept is contextual.

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For \(A(x)~=~8~+~500/x\), where \(x\) is a positive whole number of items and \(A\) is average cost in dollars per item, find the algebraic intercepts, check their feasibility, and interpret the contextual result.

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