A company manufactures and sells shirts. The daily profit the company makes
depends on how many shirts they sell. The profit, in dollars, when the company sells
z shirts can be found using the function f(x) = 10x - 100. Find and interpret the
given function values and determine an appropriate domain for the function.

A company manufactures and sells shirts The daily profit the company makes depends on how many shirts they sell The profit in dollars when the company sells z s class=

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Answer:

f(−5)= −150, meaning if the company sells -5 shirts, they would make a profit of -150 dollars. This interpretation does NOT make sense in the context of the problem.

f(7)= −30, meaning if the company sells 77 shirts, they would make a profit of −30 dollars. This interpretation makes sense in the context of the problem.

f(10.5)= 5, meaning if the company sells 10.5 shirts, they would make a profit of 5 dollars. This interpretation does NOT make sense in the context of the problem.

Based on the observations above, it is clear that an appropriate domain for the function is whole numbers (0, 1, 2, ...).

(Yes, these answers are officially correct.)

The interpret of the given function values and determine an appropriate domain for the function should be explained below:

The following information should be considered:

  • f(−5)= −150, meaning if the company sells -5 shirts, they would make a profit of -150 dollars. This interpretation does NOT make sense in the context of the problem.
  • f(7)= −30, meaning if the company sells 77 shirts, they would make a profit of −30 dollars. This interpretation makes sense in the context of the problem.
  • f(10.5)= 5, meaning if the company sells 10.5 shirts, they would make a profit of 5 dollars. This interpretation does NOT make sense in the context of the problem.

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