What's Your Function?

Part a:

In the article "Fuel Economy for New Vehicles Sets Record 24.8 MPG in 2013", the relationship is between the x-value which in this case is the month-year, and the y-value which in this case is the average miles per gallon for cars. Every month to year, the fuel efficiency of cars changes, and the average fuel economy has increased greatly over the years. This is a function because for every month/year, there is a unique output of miles per gallon. Even though multiple months(inputs) can have the same miles per gallon(output), a month(input) cannot be matched with more than one miles per gallon amount(output). This function is not linear because the graph is not represented by a straight line and the graph does not have a constant rate of change at every interval. 

This relationship between the independent variable (months) and the dependent variable (average miles per gallon for cars), shows that cars have been forced to increase their fuel efficiency over time, so the average miles per gallon for cars have been increasing over time.

As one can see, the rate of change for a few intervals below are not equal.
For Oct 2008 to Jan 2009 = 20.4-20.6/6-5 = -.2 = ROC
For Jan 2009 to Apr 2009= 21.2-20.4/7-6 = .8= ROC
For Apr 2009 to Jul 2009= 22.2-21.2/8-7= 1= ROC

This function is not a mathematical model, there is no function notation to get from x to f(x).

http://www.edmunds.com/car-news/fuel-economy-for-new-vehicles-sets-record-248-mpg-in-2013.html

Part b:

In the article "Big season paying dividends in recruiting for Azusa Pacific University football", the relationship is between the x-value, which are the area codes that the football players for Azusa Pacific football are from, and the y-value are the players. 
In this article, the relationship shows that the independent variables are the area codes from which these players are recruited from to play football, and the dependent variables are the players that become recruited. 

For example,

For the area code 626, there are multiple players recruited
For the area code 951, there are also multiple players recruited
For the area code 909, there are also many players recruited
This makes it so that for one input (area code) there are many outputs (players)

So, this is NOT a function because for every area code there is not a unique output of a player, because for one area code(input) there are multiple players(output), and for it to be a function, one area code(input) cannot be matched with more than one player(output).

http://www.sgvtribune.com/sports/20140116/big-season-paying-dividends-in-recruiting-for-azusa-pacific-university-football