Blog Post 2: What's your function? Eamon Martin

Eamon Martin

02-09-15

Blog #2: What’s Your Function?

Part A:

1.      My article is http://www.npr.org/blogs/thetwo-way/2015/01/26/381639118/2015-will-continue-streak-of-shrinking-u-s-budget-deficit

2.      A relationship is a function if a certain number of one area, variable, etc is paired with exactly one number of another.  It is not a function if it does not pass the vertical line rule, in which one value corresponds with more than one value of another variable.

3.       

4.      This graph actually displays two functions, showing the relationship between the year and the United States Federal government revenues, and the year and the United States Federal Government expenditures. 

5.      Neither are linear functions because the values of the expenditures and revenues do not increased by a fixed amount for each year that passes.

6.      It is fairly easy to prove that these graphs do not display a linear function by looking at the rate of change in different time intervals.  Between (approximately) 2008 and 2009, there was a sharp increase in spending, as seen by a steep slope in the outlay graph.  After this period however, the graph shows a negative slope as expenditures (as percentage of GDP) fell.  The rate of change in both time frames is very different.

In 2008 and 2009, revenues fell sharply as well, which can be seen with the negative slope that the graph has in that time interval.  From 2012 however, revenues increased fairly significantly, which can be seen in the positive slope on the graph.  In each, the average rate of change is significantly different.

7.      Both Revenue and Expenditures, as percentages of GDP, can be considered functions of time (year), and thus it is a mathematical model because we can use functional notation to express the relationship.

F(y)= R (for Revenue as percentage of GDP)

F(y)= E (for Expenditures as percentage of GDP)

Part B:

1.      A relationship is not a function if there is more than one output value corresponds with one input value.  This is related to the Vertical Line Test, in which a relationship is not a function if there is more than one Y value that corresponds with a single x value.

2.      *I couldn’t find a periodical that featured a relationship that wasn't a function, so I found a survey done by this website:

3.      The relationship displayed here is that of the connection between height and weight, and the connection they have.

4.      This relationship is not a function because it fails the vertical line test.  As the height of 46/47 inches, there is different weight value and a vertical line can be formed between them.  Thus, it is only a relationship, and not a function.