SOLUTION: Can someone please help me to finish this problem? Thank you. The charge to rent a trailer is $30 for up to 2 hours plus $9 per additional hour or portion on an hour. Find the c

This is a piece-wise function, and will involve 2 separate functions.

Let the cost, based on "h" hours, be C(h)

1st function:

Since it costs $30 for up to 2 hours, we get the following function: 

2nd function:

Since it costs $9 per additional hour, or a portion of, then any amount of hours GREATER than 2 hours, ROUNDED UP, will cost $9. This gives us:

C(h) = 9(h - 2) + 30_______C(h) = 9h + 12



Combining the two functions gives us: 

a) 3.7 hours

You have to ROUND UP 3.7 to 4 hours since .7 hours will cost what 1 hour costs. Therefore, we're looking at the cost to rent it for 4 hours.

For this, we look at and use the function for the cost when h > 2. This is the 2nd function. 

Therefore, we get: 



b) 4 hours

I think you realize by now that the charge for 4 hours is the same as the charge for 3.7 hours.

Therefore, for this we ALSO get: 



c) 8.6 hours

You have to ROUND UP 8.6 hours to 9 hours since .6 hours will cost what 1 hour costs. Therefore, we're looking at the cost to rent it for 9 hours.

For this, we look at and use the function for the cost when h > 2. This is the 2nd function. 

Therefore, we get: 



GRAPHING

You're graphing two (2) functions here, and BOTH will be in the 1st quadrant on the coordinate plane.

Both functions represent LINEAR equations, but there are DOMAINS and RANGES to each.



Function 1 is simply C(h) = 30, or more traditionally, y = 30. I'm sure you realize that this is a HORIZONTAL LINE that's parallel to the x-axis. 

It'll start from (0, 30), with an OPEN circle at that point, and a CLOSED CIRCLE at the end-point, or (2, 30) to signify that for $30, x or number of hours are > 0, but . 



Function 2 is simply C(h) = 9h + 12, or more traditionally, and on the xy coordinate plane, y = 9x + 12. 

Graph this as you would any LINEAR equation, but the DOMAIN (x), will start at x > 2, denoted by an OPEN CIRCLE, and there will be no end point as this line goes to + infinity.

Realistically though, there is a limit to how many hours that trailer will be rented. In other words, you wouldn't find someone/a company renting this for say 1,000, 2,000, or 10,000 hours.