Part (A)
Answers:
Independent Variable = x = number of hours
Dependent Variable = f(x) = total cost in dollars
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Step-by-step explanation:
The independent variable is always x. When dealing with time, the time value is often the independent variable as time does its own thing. It marches on without any influence or external factors to change it.
On the other hand, the total cost is affected by time. The more time goes on, the higher the total cost will be. We say the total cost is dependent on the time. The dependent variable is always y, which can be replaced with f(x). In short, y = f(x).
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Part (B)
Answer:
f(x) = 20x + 25
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Step-by-step explanation:
The flat rate of $25 represents the initial cost. This is the cost if x = 0 hours of work is done. So this is the cost to get in the door, so to speak. You can think of this as the parts cost (from "parts and labor").
On top of that initial cost is the cost of $20 per hour. This can be thought of as the labor cost. If a job takes 1 hour to do, then we add on $20 to the flat rate of $25. If it takes 2 hours, then we add on 2*20 = 40 dollars. And so on. For x hours, we add on 20x dollars. Whatever x is, we multiply by 20.
So overall we have a flat rate of $25 and a variable rate of 20x dollars giving a total cost of f(x) = 20x+25
As a check, plugging x = 0 should lead to f(x) = 25
Plugging x = 1 should lead to f(x) = 20+25 = 45
And so on.