Wheres the Function?

I found online President Obama’s approval ratings listed every day spanning the entire length of his presidency thus far. The website is :

http://www.realclearpolitics.com/epolls/other/obama_bush_first_term_job_approval.html . This is a function because for every input, the day, there is one matching output, the approval rating. It therefore passes the vertical line test. In this case, the President’s approval rating is the dependent variable. It depends on the independent, which is time (in days). The approval ratings depends on the time because over time the President makes certain decisions that can sway his ratings. One month he may have a spike in ratings due to a successful initiative and another month he may have a drop due to a blunder, like his recent MediCare site. The function in function notation would be:

 Approval Rating=f(Time)    à time in days

This function is NOT linear, because the values of the average rate of change are not identical. If the function were linear, the slope would be consistent and create a straight line when graphed. Approval ratings are variable that depend on random, independent occurrences rather than predictable, stable variables. If the function were linear, the “changes in rating” would all be the same, indicating a steady linear relationship.

            As stated earlier, this function is a mathematical model. Although some could consider it isn’t, I argue that it is. My reason being is that in this case, time in days is not just a physical date, but it is an indication of choices being made by the President. On January 17, 2014 the President has extremely poor approval ratings following his Medicare blunder. But his ratings may have been higher following healthcare reform initiatives.

            As for relationships that are not functions, I struggled to find an example but might have gotten one. When reading about professional sport’s teams uniforms, I caught something. Functions CANNOT have the same x-values. Sure, if we are looking at New York Yankees Player, Shirt Color being (x, y), this is a function. But if we change it around to Shirt Color, Player , this is no longer a function. A FUNCTION MAY NOT HAVE TWO Y-VALUES ASSIGNED TO THE SAME X-VALUE.

The article I was looking at was:

http://sports.yahoo.com/news/top-25-uniforms-worn-professional-sports-teams-years-185100394--spt.html

The relationship I was looking at was between Professional Athletes and shirt colors.