Context: A repair specialist charges $160 for the first two hours plus an hourly fee for each additional hour, and a $6$-hour repair costs $360. We need the function $f$ giving the total cost for $x$ hours, where $x\ge2$.

Answer: A) $f(x)=50x+60$

Why: A $6$-hour job has $4$ hours beyond the first two, so $160 + 4a = 360$, giving the additional-hour fee $a = 50$. Then $f(x) = 160 + 50(x - 2) = 50x + 60$. Check: $f(6) = 300 + 60 = 360$.

Traps:

• B) $f(x)=50x+160$ charges $50 for all $x$ hours on top of the $160, double-counting the first two hours; it gives $f(6) = 460$, not $360$
• C) $f(x)=60x$ just divides $360$ by $6$, assuming one flat hourly rate with no $160 base charge; it gives $f(2) = 120$ instead of $160$
• D) $f(x)=60x+160$ combines that flat $60 rate with the base fee, giving $f(6) = 520$, not $360$