Question

question 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 x shirts can be found using the function f(x)=6x - 70. find and interpret the given function values and determine an appropriate domain for the function.
answer attempt 1 out of 2
f(-2)=\square, meaning if the company sells \square shirts, they would make a profit of \square dollars. this interpretation
\vee in the context of the problem.
f(12)=\square, meaning if the company sells \square shirts, they would make a profit of \square dollars. this interpretation
\vee in the context of the problem.
f(17.5)=\square, meaning if the company sells \square shirts, they would make a profit of \square dollars. this interpretation
\vee in the context of the problem.
based on the observations above, it is clear that an appropriate domain for the function is

Explanation:

Step1: Calculate \( f(-2) \)

Substitute \( x = -2 \) into \( f(x)=6x - 70 \).
\( f(-2)=6\times(-2)-70=-12 - 70=-82 \)
The interpretation: If the company sells \(-2\) shirts (which is not possible in a real - world context as the number of shirts sold can't be negative), the profit is \(-82\) dollars.

Step2: Calculate \( f(12) \)

Substitute \( x = 12 \) into \( f(x)=6x - 70 \).
\( f(12)=6\times12-70 = 72-70=2 \)
The interpretation: If the company sells \(12\) shirts, the profit is \(2\) dollars.

Step3: Calculate \( f(17.5) \)

Substitute \( x = 17.5 \) into \( f(x)=6x - 70 \).
\( f(17.5)=6\times17.5-70=105 - 70 = 35 \)
The interpretation: If the company sells \(17.5\) shirts (in a mathematical sense, although in a real - world business, the number of shirts sold is usually an integer), the profit is \(35\) dollars.

Answer:

\( f(-2)=-82 \), interpretation: If the company sells \(-2\) shirts (not practical), profit is \(-82\) dollars.
\( f(12)=2 \), interpretation: If the company sells \(12\) shirts, profit is \(2\) dollars.
\( f(17.5)=35 \), interpretation: If the company sells \(17.5\) shirts (mathematical result), profit is \(35\) dollars.