Part A:
A relationship is a function if an input value does not contain more than one output value. In other words, there is one output for one input. When dealing with a graph, it is easy to identify a function if the graph passes the vertical line test, in which a vertical line does not touch more than one point on the graph.
With that in mind, Comichron is a website which tracks the sales figures of popular comic books. In this example, Comichron has compiled the Average Paid Circulation (or the total paid circulation) of all of the Invincible Iron Man comics sold between 1980 and 2004. The values can be found at this link and are highlighted in yellow:
http://www.comichron.com/titlespotlights/ironman.html
In this relationship, the input is time in years (1980 to 2004) and the output is the total paid circulation of Iron Man comics in that year. Therefore, Total paid Circulation (C)=f(year).
This relationship is not linear. The figures cannot be connected by a consistent rate of change. For example, from 1995-2000 the values are:
The Invincible Iron Man paid circulation:
Year: 1995--82,469
1996--64,717
1997--184,386
1998--151,476
1999--92,008
2000--69,257
There is no linear slope.
This relationship is, however, a mathematical model. The output (the average paid circulation) is dependent on the input (year) since the APC could not be calculated without the duration of the input (year).
Part B:
For part B, I am going to use the same example as Part A. However, I will change my output from the total paid circulation to total circulation. This will then include the total PAID circulation (highlighted in yellow), the total FREE circulation and the combined circulation. Thus, this relationship is no longer a function. Relationships are not functions if one input has multiple outputs. Using each form of circulation (outputs) of all Iron Man comics in relation to one year (input) gives the input 3 distinctive outputs--Paid circulation, Free circulation and Total circulation. Therefore, since the input (year) now has three outputs instead of one, the relationship is not a function.
This is a cool example. One curious aspect of the data is the spike in paid circulation in 1997 and 1998. It would be interesting to investigate why this occurred, especially because the Iron Man movie did not come out until years later.
ReplyDeleteIt's interesting that the relation between The invincible iron man paid circulation is a mathematical model. I was thinking that it would not be since the the date would not be the reason resulting in the paid circulation.
ReplyDeleteThe data is very interesting. Like Sam said, the fact that sales spiked significantly between the years 1997-1998 is odd. The external factors that caused this to occur is something that might be worth taking a look at.
ReplyDeleteYour information is very interesting and complete I like what you wrote about and finding information that is different from others
ReplyDeletetess,
ReplyDeleteyour first example is brilliant. and being a fan of comic books, i was all the more interested. you did a great job of explaining the relationship using math vocabulary.
i like the idea that you had for switching the variables around to try to make a relationship that is not a function, but given the way that you explain this, you would essentially just have three separate functions related to time. good and creative try, though.
professor little