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=25N+500 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.

Answer 1

Given:

The function is

`C=25N+500`

Find-:

(a)

Domain

(b)

Range

Explanation-:

(a)

Domain

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.

The function is:

`C=25N+500`

Where

`\begin{gathered} C=\text{ Cost of publishing book } \\ \\ N=\text{ Number of copies} \end{gathered}`

For the domain

Description of value

`=\text{ Number of copies produced}`

The domain value is:

The company produces 300 copies than the domain

`\text{ Domain }=\lbrace0,1,2,3,................,300\rbrace`

(b)

Range

The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs. In the function machine metaphor, the range is the set of objects that actually come out of the machine when you feed it all the inputs.

For the range

Description of value

`=\text{ Cost of publishing book}`

The range value is:

`C=25N+500`

At N = 0 value is:

`\begin{gathered} C=25N+500 \\ \\ N=0 \\ \\ C=25(0)+500 \\ \\ C=500 \end{gathered}`

At N = 300 value is:

`\begin{gathered} C=25N+500 \\ \\ N=300 \\ \\ C=25(300)+500 \\ \\ C=7500+500 \\ \\ C=8000 \end{gathered}`

So, the value of the range is

`=\lbrace500,525,550,.............,8000\rbrace`