Question

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.

Which statement describes the limitation for the reasonable range compared to the mathematical range?

The reasonable range is limited to the whole numbers when 0 ≤ y ≤ 12,000.
The reasonable range is limited to the rational numbers when 0 ≤ y ≤ 12,000.
The reasonable range is limited to the whole numbers when 0 ≤ y ≤ 144,000.
The reasonable range is limited to the rational numbers when 0 ≤ y ≤ 144,000.

Answer 1

The reasonable range is limited to the whole numbers when 0 ≤ y ≤ 144,000.

Explanation:

Notice that even though the range of the function is mathematically defined for all real numbers, in the real world you can't have more than 144,000 granola bars; that occurs when you have no boxes, or in other words, when x = 0

On the other hand, in the real word you can't have a negative quantity of a thing (you can't have minus 2 popsicles, for example). Given that granola bars are things, you must have at least 0 granola bars; in other words the quantity of granola bars must be greater or equal zero.

We know that in the real word you cant have more than 144,000 granola bars, and you must have at least 0 granola bars; therefore, the reasonable range of the function f(x) = –12x + 144,000 is 0 ≤ y ≤ 144,000.

Since we are talking of full granola bars here, the range is limited to whole numbers (whole granola bars).

We can conclude that the correct answer is: The reasonable range is limited to the whole numbers when 0 ≤ y ≤ 144,000.