Question

Elude has 65 water bottles for the 5K race participants in addition, he is planning to buy some boxes of water bottles that have 14 water bottles each. All of the boxes cost the same. Elude is not sure yet about the number of boxes of water bottles he wants to buy, but he has enough money to buy five of them. Write a function to describe how many water bottles Elude can buy. Let X represent the number of boxes of water bottles. Find a reasonable domain and range for the function.

a) f(X) = 65 + 14X, Domain: {0, 1, 2, 3, 4, 5}, Range: {65, 79, 93, 107, 121, 135}
b) f(X) = 65 + X/14, Domain: {0, 1, 2, 3, 4, 5}, Range: {65, 66, 67, 68, 69, 70}
c) f(X) = 65 * 14X, Domain: {0, 1, 2, 3, 4, 5}, Range: {0, 910, 1820, 2730, 3640, 4550}
d) f(X) = 65 - 14X, Domain: {0, 1, 2, 3, 4, 5}, Range: {65, 51, 37, 23, 9, -5}

Answer 1

The correct function for the number of water bottles Elude can buy is f(X) = 65 + 14X with a domain of {0, 1, 2, 3, 4, 5} and a range of {65, 79, 93, 107, 121, 135}.

Step-by-step explanation:

The question involves writing a function to describe how many water bottles Elude can buy. Given Elude starts with 65 bottles and may buy additional boxes, each containing 14 water bottles, we are to consider the function f(X) = 65 + 14X. Here, X represents the number of additional boxes Elude decides to buy. Since Elude has enough money to buy up to five boxes, the domain of our function (the possible values of X) is {0, 1, 2, 3, 4, 5}. The range is determined by plugging each domain value back into the function, resulting in the set {65, 79, 93, 107, 121, 135}.