Each person who enters a store receives a $5 off coupon. In the equation y = 5x, y is the total value of the coupons given out by the store, and x is the number of people receiving the coupons.

Wen says the function is continuous, because the number of people is unlimited. Is Wen right or wrong? Explain.

Question

Each person who enters a store receives a $5 off coupon. In the equation y = 5x, y is the total value of the coupons given out by the store, and x is the number of people receiving the coupons.

Wen says the function is continuous, because the number of people is unlimited. Is Wen right or wrong? Explain.

Mercury · Answer

Please do not copy-paste my answer. Whether a function is continuous or not depends on what values the domain can take. Because the # of people can only take nonnegative integers, the function is discrete, even if the domain extends to infinity.