Question

a small publishing company is planning to publish a new book. let c be the total cost of publishing the book (in dollars). let n be the number of copies of the book produced. for the first printing, the company can produce up to 200 copies of the book. suppose that c = 10n + 800 gives c as a function of n during the first printing. 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. domain: description of values number of copies produced cost of publishing book (in dollars) set of values select range: description of values number of copies produced cost of publishing book (in dollars) set of values the set of all real numbers from 0 to 800 the set of all real numbers greater than 200 the set of all real numbers greater than 10 {0, 1, 2, 3, ..., 200} {10, 20, 30, 40, ..., 800} {800, 810, 820, 830, ..., 2800}

Explanation:

Step1: Define domain

The domain is the set of input values. Here, $N$ represents the number of copies produced and it can range from $0$ to $200$ (in whole - numbers as you can't produce a fraction of a book), so the domain is $\{0, 1, 2,\ldots, 200\}$.

Step2: Define range formula

The cost function is $C = 10N+800$. When $N = 0$, $C=10\times0 + 800=800$. When $N = 200$, $C=10\times200+800=2000 + 800=2800$. As $N$ takes values from $0$ to $200$ in steps of $1$, $C$ takes values $C = 10N+800$ where $N\in\{0, 1,\ldots, 200\}$, so the range is $\{800, 810,\ldots, 2800\}$.

Answer:

Domain - Description of Values: number of copies produced
Domain - Set of Values: $\{0, 1, 2, 3,\ldots, 200\}$
Range - Description of Values: cost of publishing book (in dollars)
Range - Set of Values: $\{800, 810, 820, 830,\ldots, 2800\}$