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Answer:
f(x) = {0, x≤ 1; 4(x -1), 1 < x ≤ 6; 2.5x +5, x > 6}
Step-by-step explanation:
The hourly rate gives you the slope of the function in the relevant interval. The added constant is chosen to make the function continuous.
That is, at 1 hour, the charge is zero, so the next segment (4x+b) must have a value of b that makes the charge for 1 hour be zero. That will be b=-4.
Likewise, for more than 6 hours, the charge will be (2.5x+b), where b is chosen to make this expression match the charge for 6 hours. We know the charge for 6 hours is 4(6) -4 = 20, so b must match ...
2.5(6) +b = 20
b = 20 -15 = 5
The segment from 1 to 6 hours is f(x) = 4x -4.
The segment for more than 6 hours is f(x) = 2.5x +5.
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<em>Alternate solution</em>
Since the charge is zero for the first hour, the first segment could be considered to be charging only for hours after the first. That is, an alternate expression for hours 1–6 could be 4(x -1). Likewise, we could say the expression for hours more than 6 is 2.5(x +2).
