Question

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 $12,000 per year, what effect does this have on the graph of the cost function?

Answer 1

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.