Final answer:
The domain of Frank's pay function is {0, 1, 2, ..., 110}, which represents the number of copies he can sell, while the range is {3600, 3630, 3660, ..., 6900}, representing the total pay he can earn based on sales.
Step-by-step explanation:
The domain of the function p = 30n + 3600, which represents Frank's total pay p, as a function of the number of copies of 'History is Fun' sold n, is the set of all possible values that n can take. Given that Frank has 110 copies available, the domain of n would be the whole numbers from 0 to 110, since he cannot sell a negative number of copies, nor can he sell more copies than he has. Therefore, the domain is n = {0, 1, 2, ..., 110}.
The range of the function is the set of all possible values for p. Since p depends on n, for each copy sold, Frank earns $30, so the smallest amount he can earn is when he sells no copies, which would be just the base pay of $3600. The largest amount he would make is if he sold all 110 copies, which would be p = 30 * 110 + 3600 = 6900. Thus, the range of p is {3600, 3630, 3660, ..., 6900}.
In summary, the domain and range for the function p = 30n + 3600 given Frank's sales conditions are discrete sets of values. The domain is the set of whole numbers from 0 to 110 (the number of copies he can sell), and the range is the set of values for p starting at $3600 (when no copies are sold) going up in increments of $30 to a maximum of $6900 (when all 110 copies are sold).