To carefully analyze the given function [tex]\( C = 20N + 500 \)[/tex] for the first printing of a book by the publishing company:
1. Identify the Domain and Range:
- Domain: The domain corresponds to the input values of the function, which, in this case, are the possible values of [tex]\( N \)[/tex] (the number of copies produced).
- Range: The range corresponds to the output values of the function, which, in this case, are the possible values of [tex]\( C \)[/tex] (the cost of publishing the book in dollars).
2. Descriptions and Values for the Domain:
- Description of Values for the Domain: The domain represents the "number of copies produced."
- Set of Values for the Domain: Since the company can produce up to 100 copies during the first printing, the number of copies produced, [tex]\( N \)[/tex], ranges from 1 to 100.
3. Descriptions and Values for the Range:
- Description of Values for the Range: The range represents the "cost of publishing book (in dollars)."
- Set of Values for the Range: We calculate the minimum and maximum cost based on the number of copies produced:
- Minimum Cost: When [tex]\( N = 1 \)[/tex]:
[tex]\[
C = 20 \times 1 + 500 = 520 \text{ dollars}
\][/tex]
- Maximum Cost: When [tex]\( N = 100 \)[/tex]:
[tex]\[
C = 20 \times 100 + 500 = 2500 \text{ dollars}
\][/tex]
Therefore, the range of the cost of publishing the book, [tex]\( C \)[/tex], is from 520 to 2500 dollars.
Combining all the information, we have:
[tex]\[
\begin{tabular}{|l|l|l|}
\hline & \text{Description of Values} & \text{Set of Values} \\
\hline \text{Domain:} & \text{number of copies produced} & 1 \text{ to } 100 \\
\hline \text{Range:} & \text{cost of publishing book (in dollars)} & 520 \text{ to } 2500 \\
\hline
\end{tabular}
\][/tex]
