You are buying party favors that cost $2.47 each. You can spend no more than $30 on party favors. What domain and range are reasonable for this situation?
For this situation, the domain refers to the possible number of party favors that can be bought, and the range refers to the total cost of the party favors.
Domain: The number of party favors must be a positive whole number since it wouldn't make sense to buy a fraction or negative amount of party favors. Additionally, the number of party favors should be within a reasonable range considering it is a party and the budget is $30. Assuming the person buying the party favors wants to have a variety of items, it would be reasonable to consider a minimum of 5 party favors (likely more) and a maximum of 15 party favors (likely less than 20). Therefore, the domain is {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}.
Range: The range represents the cost of the party favors. The minimum possible total cost is when just 1 party favor is purchased, which would be $2.47. The maximum possible total cost is when the person buys 15 party favors, which would be $37.05, exceeding the maximum budget of $30. Therefore, the range is {2.47, 4.94, 7.41, 9.88, 12.35, 14.82, 17.29, 19.76, 22.23, 24.70, 27.17, 29.64}. However, the range values greater than $30 (such as 37.05) are not reasonable in this situation as the budget cannot be exceeded. Therefore, a more reasonable range would be {2.47, 4.94, 7.41, 9.88, 12.35, 14.82, 17.29, 19.76, 22.23, 24.70, 27.17, 29.64} (rounding the values down to the nearest cent).