Subjects algebra

Cost Function 77C7De

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1. **State the problem:** We are given the function $$C = 25N + 600$$ where $$C$$ represents the cost of publishing a book and $$N$$ represents the number of copies produced. 2. **Identify the domain:** The domain is the set of all possible values for $$N$$, the number of copies produced. Since you cannot produce a negative number of copies, $$N$$ must be a whole number starting from 0 and going upwards. So, the domain is $$\{0, 1, 2, 3, \ldots\}$$. 3. **Identify the range:** The range is the set of all possible values for $$C$$, the cost. Using the domain values, the minimum cost is when $$N=0$$, which gives $$C = 25 \times 0 + 600 = 600$$. As $$N$$ increases by 1, $$C$$ increases by 25. So the range is $$\{600, 625, 650, 675, \ldots\}$$. 4. **Summary:** - Domain: number of copies produced $$N$$ is $$\{0, 1, 2, 3, \ldots\}$$. - Range: cost $$C$$ is $$\{600, 625, 650, 675, \ldots\}$$. This matches the options: - Domain corresponds to "number of copies produced". - Range corresponds to "{600, 625, 650, 675, ..., 8100}" (or continuing upwards). Hence, the function is linear with domain as non-negative integers and range as costs starting at 600 and increasing by 25 for each additional copy.