a) You need to write the cost function using the information provided by problem, that links the number of people and admission price such that:

`C(n) = 0.75*n + 5*3 + 8*2`

`C(n) = 0.75*n + 15 + 16`

`C(n) = 0.75*n + 31`

Hence, evaluating the equation describing the cost of the familiy going to the fair yields `C(n) = 0.75*n + 31` .

b) Notice that the domain of the function comprises the values of n that represents the number of raffle tickets bought. Hence, the number of the tickets bougth can not be negative. If there are no tickets bought, then n = 0.

Hence, the domain of the function comprises the number of tickets bougth such that: `[0,oo).`

c) The range of the function may be found substituting all values from domain for n in equation `C(n) = 0.75*n + 31` , hence for n = 0 => `C(0) = 31.75` .

Hence, the interval `[31.75 , oo) ` expresses the range of the function.