A factory has a linear cost function f(x)= ax+b , where b represents fixed costs and a represents the labor and material costs of making one item, both in thousands of dollars. If property taxes (part of the fixed costs) are decreased by ,000 per year, what effect does this have on the graph of the cost function?

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Answer: the effect is to bring the graph of the original cost function, f(x) 12 units downward. Explanation: 1) Being the original cost function f(x) = ax + b, if property taxes, which are part of the fixed costs, are decreased by $12,000 per year, the new cost function will be: g(x) = ax + b - 12 ↔ note that I use 12 and not 12,000 thousands, because b and a are told to represent costs in thousands of dollars. Therefore, g(x) = f(x) - 12. Meaning that the effect is to shift the graph of the original cost function, f(x) 12 units downward.


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