What's Your Function

Part A

1. I searched the Economist (magazine) website for articles
2. A function is a function when one input is paired with exactly one and only one output, and its graph passes the vertical line test.
3. The graph I selected that demonstrates a function comes from an article called "Musical Chairs" about British Unemployment. For the sake of this assignment, I will only be looking at Percent Unemployed related to the Year (red line).

4. The graph represents the Civilian unemployment rate in each quarter (3 months) of each year in Britain from 2005-2014. Q1 stands for Quarter 1, Q3 for Quarter 3, and so on. 

5. The relationship is not linear. 

6. n/a 

7. Between each quarter, there are several variations in rates of change. for example, the original unemployment rate in Q1 of 2005 was roughly 4.75%. In Q3 of 2014, it was roughly 6%. Therefore, the rate of change was 2% over 9 years and 2 quarters, or 9.5 years. Therefore, the average rate of change is 0.2/9.5 or 0.021. This is a much smaller rate of change than that of Q1 of 2008 to Q3 of 2009, where the unemployment rate increases almost 3% in just 1.5 years, with a rate of change of 0.2(0.3/1.5). We know this is not a linear function because the Average Rate of Change is not equal to any rate of change between two given points on the graph. 

8. Yes, this is a mathematical model, although it is debatable amongst Economists. Most, however, would agree that the unemployment rate is a function of time, because as economic conditions improve or worsen, the market fluctuates and more or less people become employed. 

Part B

This graph represents the relationship between height and wealth in the Netherlands over time. The graph shows that over time, as wealth grows, people also have become taller in the Netherlands. This is perhaps suggesting that as a society develops and earns more money, its people become healthier and grow faster and taller.  It is not a function because income was the same in years at the beginning of the graph, as well as somewhere between 1918 and 1940. It is also quite likely that income was the same in 1870 as 1918. This graph therefore has multiple outputs per input, and is not a function.