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A business owner purchased an energy-efficient air conditioning system for a cost of $\$4,200$, including installation. The business owner saves $\$940$ per year to operate the new system compared to the operating cost of the old system. Including the cost of the new system, which function $f$ gives the total amount, in dollars, the business owner has saved $x$ years after purchasing the new system?

A

$f(x)=-4,200x+940$

B

$f(x)=-940x-4,200$

C

$f(x)=940x-4,200$

D

$f(x)=4,200x-940$