The function f(x) = –12x + 144,000 is used to model the number of granola bars in stock depending on the number of boxes, x, one machine packages if the machine starts with 144,000 granola bars. The mathematical range for the function is the set of real numbers.
Answer
A
The reasonable range is limited to the whole numbers when 0 ≤ y ≤ 12,000.
B
The reasonable range is limited to the rational numbers when 0 ≤ y ≤ 12,000.
C
The reasonable range is limited to the whole numbers when 0 ≤ y ≤ 144,000.
D
The reasonable range is limited to the rational numbers when 0 ≤ y ≤ 144,000.
Explanation
The machine starts with 144,000 bars, and each box packaged reduces the stock by 12 bars. It can package at most 144,000 ÷ 12 = 12,000 boxes, so the stock ranges from 144,000 down to 0. Since the number of bars is counted in whole numbers, the reasonable range is whole numbers from 0 to 144,000: choice C.
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