Write A Piecewise Function From A Word Problem

Question

Shipping company IPS has shipping rates that are a function of the weight of the parcel. For packages weighing less than or equal to 5 pounds, they charge $ 1 per pound. For packages weighing between 5 and 10 pounds, they charge $ 2 per pound. If packages weigh 10 pounds or more, they charge $ 2.75 per pound. IPS refuses to ship any parcel weighing more than 51 pounds. There is also a flat fee of $ 1 for all deliveries and an additional fee of $ 3 for all deliveries weighing 10 pounds or more.

Complete the following description of a piecewise function so that it describes the shipping costs C(x) in dollars as a function of the weight x in pounds.

C(x)= {... if x is in the interval ...
{... if x is in the interval ...
{... if x is in the interval ...

Answer 1

where x is the weight of the package with domain 0 < x < = 51

C(x) =

{

x+1 if x<=5,

2x +1 if 5 < x < 10,

2.75x+4 if 10 <=x <=51

}