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Choice A is correct. It’s given that the window repair specialist charges $\$220$ for the first two hours of repair plus an hourly fee for each additional hour. Let $n$ represent the hourly fee for each additional hour after the first two hours. Since it’s given that $x$ is the number of hours of repair, it follows that the charge generated by the hourly fee after the first two hours can be represented by the expression $n\left(x-2\right)$. Therefore, the total cost, in dollars, for $x$ hours of repair is $f\left(x\right)=220+n\left(x-2\right)$. It’s given that the total cost for $5$ hours of repair is $\$400$. Substituting $5$ for $x$ and $400$ for $f\left(x\right)$ into the equation $f\left(x\right)=220+n\left(x-2\right)$ yields $400=220+n\left(5-2\right)$, or $400=220+3n$. Subtracting $220$ from both sides of this equation yields $180=3n$. Dividing both sides of this equation by $3$ yields $n=60$. Substituting $60$ for $n$ in the equation $f\left(x\right)=220+n\left(x-2\right)$ yields $f\left(x\right)=220+60\left(x-2\right)$, which is equivalent to $f\left(x\right)=220+60x-120$, or $f\left(x\right)=60x+100$. Therefore, the total cost, in dollars, for $x$ hours of repair is $f\left(x\right)=60x+100$.

Choice B is incorrect. This function represents the total cost, in dollars, for $x$ hours of repair where the specialist charges $\$340$, rather than $\$220$, for the first two hours of repair.

Choice C is incorrect. This function represents the total cost, in dollars, for $x$ hours of repair where the specialist charges $\$160$, rather than $\$220$, for the first two hours of repair, and an hourly fee of $\$80$, rather than $\$60$, after the first two hours.

Choice D is incorrect. This function represents the total cost, in dollars, for $x$ hours of repair where the specialist charges $\$380$, rather than $\$220$, for the first two hours of repair, and an hourly fee of $\$80$, rather than $\$60$, after the first two hours.