Wen is not entirely correct in saying that the function is continuous because the number of people is unlimited. While it is true that the store can give out coupons to an unlimited number of people, the situation at hand involves discrete quantities—specifically, the number of people receiving coupons (x) is a discrete variable, as you cannot have a non-integer number of people.
The equation \( y = 5x \) indeed defines a linear relationship between \( y \), the total value of the coupons, and \( x \), the number of people. However, since \( x \) can only take on whole numbers (0, 1, 2, 3, ...), the values of \( y \) will also be discrete multiples of 5 (0, 5, 10, 15, ...).
Therefore, the function \( y = 5x \) is not continuous in the mathematical sense, because continuity requires the ability to take on any value within an interval (including non-integer values), which does not occur here. Instead, the function is defined at specific points corresponding to whole numbers of people.
In conclusion, the function is a discrete function, and thus Wen is incorrect in claiming that it is continuous.
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