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 300 copies of the book. suppose that c = 20n+700 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.

	description of values	set of values
range:	number of copies produced<br>cost of publishing book (in dollars)	the set of all real numbers from 0 to 700<br>the set of all real numbers greater than 300<br>the set of all real numbers greater than 20<br>{700, 720, 740, 760, ..., 6700}<br>{0, 1, 2, 3, ..., 300}<br>{20, 40, 60, 80, ..., 700}

Explanation:

Step1: Define domain

The domain of a function is the set of all possible input values. Here, the input variable is $N$ which represents the number of copies produced. The company can produce up to 300 copies and the number of copies cannot be negative or a non - integer in this context. So the domain is the number of copies produced and the set of values is $\{0,1,2,\cdots,300\}$.

Step2: Define range

The range of a function is the set of all possible output values. The function for the cost $C = 20N+700$. When $N = 0$, $C=20\times0 + 700=700$. When $N = 300$, $C=20\times300+700=6000 + 700=6700$. As $N$ takes integer values from 0 to 300, $C$ will take values $C = 20N+700$ where $N\in\{0,1,\cdots,300\}$. So the range is the cost of publishing the book (in dollars) and the set of values is $\{700,720,740,\cdots,6700\}$.

Answer:

Domain:

• Description of Values: number of copies produced
• Set of Values: $\{0,1,2,\cdots,300\}$

Range:

• Description of Values: cost of publishing book (in dollars)
• Set of Values: $\{700,720,740,\cdots,6700\}$