Question

First six shipments:
10, 16, 22, 28, 34, 40
A factory is producing a linear number of objects in each shipment. If x = the shipment number, which function can be used to determine how many objects are in that shipment?

Answer 1

For problems like this, we need to find the pattern between the set of numbers to create a general equation for f(x). Given that x is the shipment number, let us first observe the first six shipments' behavior.
1  10 |
2  16 = 10 + 1(6) |
3  22 = 10 + 2(6) |
4  28 = 10 + 3(6)|  
5  34 = 10 + 4(6) |
6  40 = 10 + 5(6) |

From these, we can observe that given x number of shipments, the total number of objects would be $10 + (x-1)6 = 10 + 6x - 6 = 6x +4$. Thus, given f(x), we have 

$f(x) = 6x + 4$
Answer: f(x) = 6x + 4