Professor Little
Applied Precalc
October 7 2014
Blog Post #2- Whats your Function?
Part A:
1 1.) The periodical that I choose is from online and it shows Lebron James' stats for his average playing time for each season in his career thus far (2003-Present). The website, ESPN, shows the statistics of any pro basketball player in the NBA as well as the statistics of other professional sports teams and their players. Almost anything related to sports ranging from Basketball to Hockey is including on the website.
2.) The definition of a function is a relationship in which one output is matched with exactly one input. That is the definition of a function in mathematical terms.
3.)The Periodical that I found can be found on ESPN.com under NBA tab and then by searching Lebron James in the search tab, where it will give you detailed stats on the player himself . It shows Lebron James' career statistics from his rookie season to the current seasons. (Excluding the 2014-2015). From my periodical the relationship shows the function is related to season average minutes played and its corresponding total percent of points made for that season, which is further represented in the table below:
4.) The following graph of Lebron's scoring percentage from his rookie year to present represents a function. For the following function, for each season's average playing time played by Lebron James(input), there was a percent total points made of attempted shots.(output). In other words for every season that Lebron James played the game of basketball, his average playing time had a specific percentage of total points made for that accounted season.
5.) After looking at both the inputs and outputs of this periodical I have come to the conclusion that it is not a function.
6.) The fact that it is not a linear function can be determined by the rate of change is different at every interval.
Rate of change: 2003-2004 season and 2004-2005 season is: 52.72
Rate of change: 2004-2005 season and 2005-2006 season is: 12.5
Rate of change: 2005-2006 season and 2013-2014 season is: -1.0 x 10^2
7.) A represents the average minutes played each season, while P represents the average percent of shots made during that season.
F(A)=P
8.) This is not a mathematical model because each season his average time of playing in the games did not have an impact on how many points he would score. Take a look at an example such as that of the two seasons: 2003-2004 and the 2008-2009. In 2003-2004 Lebron played on average of about 39.5 minutes and scored a field goal percentage of .417 goals and in the 2008-2009 season he played an average of 37.7 minutes and scored a high average of .489 goals. Therefore, this proves my theory that the output does not depend on the input.
Part B
1.) If there is a relationship in which one of the inputs is matched with more than a single one output it is then considered to not be a function.
2.) http://www.statcrunch.com/5.0/viewreport.php?reportid=30356&groupid=1422
3.) This shows the shoe sizes for people who may be tall, short, skinny, fat but all have the same shoe size regardless of their appearance. A person who is 5 feet 8 inches tall and weigh 205 pounds, may have the same exact shoe size as a person who is 5 feet 5 inches tall and only weighs about 145 pounds.
4.)This relationship is not a function due to the fact that for every shoe size a person can come in all sorts of different shapes and sizes themselves. A certain input may even have some of the same outputs so it would not pass the vertical line test if graphed. There are many possibilities for weight, height, and color for the same shoe size. Each and every input (height for example) is matched with more than one output (the wide arrange of different shoe sizes) And with that, this would then be considered not to be a function.
I really liked the example you used for the linear function. It is easy to comprehend and I like that you took the time to show the calculations to prove that it is not a linear function. The example you chose for your non-linear function also shows your understanding of the topic, as it is a very clear study due to there only being one shoes size. Good job!
ReplyDeleteI enjoyed your blog and how you really explain how it is not a linear function. You did great job proving that with ROC.
ReplyDeletethe example that you give for part b is very interesting! You also give a very good explanation about why those graphs would not be considered linear functions.
ReplyDeleteadrian,
ReplyDeletei am guessing that you meant to say that the first example is "not a linear function" instead of "not a function. excellent job of showing ROC calculations to prove non-linearity! also, good job of remembering to use function notation.
your second example is absolutely not a function! good job!
professor little