Blog Post #2

What’s your function?

Blog Post #2:

Part A:

1. The online periodical that I found is from the website: http://int.soccerway.com/.  This website shows almost anything related to soccer including match schedules, past game scores and player career statistics.

2. A function is a relationship in which one output is matched with exactly one input. 

3. The Periodical that I found can be found in the following link: http://int.soccerway.com/players/cristiano-ronaldo-dos-santos-aveiro/382/.  It shows the career statistics of Cristiano Ronaldo in the domestic leagues he has participated in from 2003 up until today. (Excluding the 2014-2015 season since it is not fully complete).  From this periodical, the relationship that I found that is a function is related to playing time in minutes and goals scored which can be shown in the table below:

Season	Playing Time In Minutes (Input)	Goals Scored (Output)
2003/2004	1548	4
2004/2005	2424	5
2005/2006	2286	9
2006/2007	2725	17
2007/2008	2746	31
2008/2009	2748	18
2009/2010	2470	26
2010/2011	2914	40
2011/2012	3353	46
2012/2013	2718	34
2013/2014	2540	31

4. For the following function, for each number of minutes played by Cristiano Ronaldo per season (input), there was a certain amount of goals scored(output).  Or, for every amount of goals scored per season, a specific amount of minutes were played that season. 

5. This function is not a Linear Function. 

 

6. The fact that this function is not linear can be determined by the fact that the rate of change at every interval is not same. 

-Rate of change between the 2003-2004 season and the 2004-2005 season is approximately: 1.14 x10^-3

- Rate of change between the 2004-2005 season and the 2005-2006 season is approximately: -0.03

- Rate of change between the 2005-2006 season and the 2006-2007 season is approximately: 0.02

7. T = Time Played in minutes

G= Goals Scored

F(T)=G

The number of goals scored is a function of the time played by Cristiano Ronaldo.  This function is not a mathematical model.  Although one would most certainly believe that the more time played would mean a higher number of goals scored, this is not the case in this function.  Take a look at the 2008-2009 and the 2009-2010 season.  In 2008-2009 Cristiano played 2748 minutes and scored 18 goals and in the 2009-2010 season he played 2470 minutes and scored 26 goals.  Therefore, the output does not depend on the input.  Other factors could have come into play, such as the fact that he played for a different team or maybe the role he had in the 2009-2010 season was a more attacking and goal scoring one.        

Part B:

1. If there is a relationship in which one input is matched with more than one output it is not a function.     

2. http://www.rush.edu/health-wellness/quick-guides/what-healthy-weight

3. This shows the range of weights for people who are considered normal, overweight and obese for a specific height.

4. The reason why this relationship is not a function is that for every height there are a vast number of possible weights for a specific height.  In other words, every input (height) is matched with more than one output (weight) therefore making the following relationship not a function.