Interpret terms, factors, and coefficients in polynomial and rational expressions.
Interpret rational numerator, denominator, quotient units, and domain
Problem
Average cost is \(C(x)~=~(500~+~8x)/x\), where the numerator is total cost in dollars and \(x\) is the number of items. Interpret the numerator, denominator, quotient units, algebraic exclusion, and contextual domain.
Big Picture
What this problem is really about
Name the numerator and denominator quantities before interpreting their quotient. The units divide in that same order, so the top quantity is measured per one unit of the bottom quantity. Keep domain reasoning in two layers: algebra forbids a zero denominator, while the context may further restrict a count to positive whole numbers rather than all nonzero reals.
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