Part A
Im ESPN we can find the career statistics of Cristiano Ronaldo and how many goals he has scored since the 2003/2004 season (his first season as a professional soccer player) until the 2013/2014 season (the current season). We can recall that a function exists when every input has exactly one output. So, the 2003/2004 season was season 1 and the current season is season 11. The data is as follows:
Season 1: 0 goals
Season 2: 9 goals
Season 3: 12 goals
Season 4: 26 goals
Season 5:43 goals
Season 6: 35 goals
Season 7: 33 goals
Season 8: 56 goals
Season 9: 71 goals
Season 10: 62 goals
Season 11: 43 goals (so far)
We can see that each input is assigned to exactly one output, making it a function. We can also observe that this is not a linear function because the rate of change is not constant.
(9-0)/(2-1)= 9
(12-9)/(3-2)= 3
They are not linear because the average rate of change is not constant.
Yes, this is a mathematical model because Cristiano's goals per season improved over the years. The out=put depends on the input. For whatever reason, his performance depended on the years.
y= 5.9455x-0.2182
http://espnfc.com/player/_/id/22774/cristiano-dos-santos-aveiro-ronaldo?cc=5901
Part B
We can recall that a relationship is not a function when every input does not have exactly one output. An example of a relationship that is not a function is a perfectly inelastic demand curve in economics.
http://www.bized.co.uk/reference/diagrams/Perfectly-Inelastic-Demand-Curve
An inelastic demand curve means that if the price of a good were to increase/decrease, people would still consume the same amount of the product/good.
We know this is not a function because when you plot it on a graph, it does not pass the vertical line test. You cannot determine the specific price from the quantity because a certain quantity has multiple price ranges.
Im ESPN we can find the career statistics of Cristiano Ronaldo and how many goals he has scored since the 2003/2004 season (his first season as a professional soccer player) until the 2013/2014 season (the current season). We can recall that a function exists when every input has exactly one output. So, the 2003/2004 season was season 1 and the current season is season 11. The data is as follows:
Season 1: 0 goals
Season 2: 9 goals
Season 3: 12 goals
Season 4: 26 goals
Season 5:43 goals
Season 6: 35 goals
Season 7: 33 goals
Season 8: 56 goals
Season 9: 71 goals
Season 10: 62 goals
Season 11: 43 goals (so far)
We can see that each input is assigned to exactly one output, making it a function. We can also observe that this is not a linear function because the rate of change is not constant.
(9-0)/(2-1)= 9
(12-9)/(3-2)= 3
They are not linear because the average rate of change is not constant.
Yes, this is a mathematical model because Cristiano's goals per season improved over the years. The out=put depends on the input. For whatever reason, his performance depended on the years.
y= 5.9455x-0.2182
http://espnfc.com/player/_/id/22774/cristiano-dos-santos-aveiro-ronaldo?cc=5901
Part B
We can recall that a relationship is not a function when every input does not have exactly one output. An example of a relationship that is not a function is a perfectly inelastic demand curve in economics.
http://www.bized.co.uk/reference/diagrams/Perfectly-Inelastic-Demand-Curve
An inelastic demand curve means that if the price of a good were to increase/decrease, people would still consume the same amount of the product/good.
We know this is not a function because when you plot it on a graph, it does not pass the vertical line test. You cannot determine the specific price from the quantity because a certain quantity has multiple price ranges.
Nice work. I like the explanation of part b because you mentioned the vertical line test.
ReplyDeleteNice integration of Math and Econ in part b!
ReplyDeleteI like how you wrote out a table to show how each output matched to one input it was helpful in you explanation.
ReplyDeletea very interesting player
ReplyDeleteNot a huge soccer fan but your stats were awesome and your ROC and formula were easy to follow. Your second example was awesome, and I love how you explained in full all the requirements for not being a function as you described it!
ReplyDelete"I'm proud to play for Real Madrid because I have fun; when you no longer have fun it's a sign that it's time to leave. For now though, I'm happy here at the greatest club in the world" Cristiano Ronaldo
ReplyDeletelaith,
ReplyDeletei love your first example! my nephews are heavily into soccer so i am familiar with some of the players. your explanations were accurate and well explained.
and nice job on the second example. that is clearly a real-life relationship that is not a function.
professor little