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Frank is a software salesman. let p be frank's total pay (in dollars). let n be the number of copies of history is fun he has sold. frank has 110 copies available to sell. suppose that p= 30n 3600 gives p as a function of n for these available copies. identify the correct description of the values in both the domain and range of the function. then, for each, choose the most appropriate set of values.

User Dmatson
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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).

User Binzi Cao
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