The graph of the revenue function f(x) = –2x2 + 100x is shown to the left. In the function, revenue is dependent on the number of items sold, x. How do the mathematical and reasonable domains compare?

Because f(x) = −2x² + 100x is a polynomial, its mathematical domain is all real numbers, −∞ < x < ∞. For a reasonable domain, the number of items sold cannot be negative, and revenue should not be negative. Solving −2x² + 100x ≥ 0 gives x(100 − 2x) ≥ 0, so 0 ≤ x ≤ 50. Therefore, choice C is correct.

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