A school bus and its driver can be rented for one day for $350. The capacity of each bus is 60 students.  http://postimage.org/image/c8xixac3r/Discrete Functions

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embizze eNotes educator| Certified Educator

Given that the capacity of a bus is 60 students, the cost of renting the bus is $350, and the number of students `n` :

(a) We need an expression for the cost of school bus rental in terms of `n` :

`C=|~n/360~|*350` where `|~~|` is the ceiling function -- it represents the whole number greater than or equal to the argument.


(c) This is the ceiling function. Usually this is called a step function -- perhaps a piecewise constant function.

(d) For the cost in terms of the number of buses `b` we have:`C=350b` for `binNN` (`binNN` means that `b` is a natural, or counting number. 0,1,2,3,... If your book doesn't allow 0 to be a natural number, you could have `bin ZZ,b>=0` which says that `b` is a nonnegative integer)



(f) This is a scatterplot. It is a linear function whose domain is the nonnegative integers.

(g) This is an opinion question -- to me the first graph makes the information easier to get.

In the first graph you can tell the range of number of students and the cost of the buses. You can infer the number of buses if you label the axes as I did -- there is one bus per line.

In the second graph you know the number and cost of the buses. From the number of buses you can infer the number of students, but this involves some arithmetic; the number of students n for k buses is `(k-1)60 lt n <= k60` .