January the 17th Blog Post - What is Your Function?

Part A:

            The article I discovered to represent a relationship that is not a functional one comes from the article Tuition at Public Colleges Rises 4.8% by Kim Clark. This article goes on to discuss the changing tuition rates for both private and public universities in the United States today. As graph 1.2 shows below the relationship between the average rate of increase in price of college tuition from 1986-1987 and spanning until 2012-2013.

            I believe this graph displays a function relationship for reasons listed below:

                        1. For every input in the graph, there is a singular output.

                        2. It passes the vertical line test; there is no way that a vertical line could accurately fit on this graph.

                        3. It is impossible for the graph to have a multitude of outputs.

                        4. The functional relationship would be displayed as C (College Tuition Rate) = f Y (Year)

                        5. Lastly, a single output cannot be paired with more than one input, as the graph displays with its multiple lines.

The graphic displayed below is a linear function because of all the above reasons.

 Graph 1.1 – College Tuition Rates 1986-2004

Article link: http://money.cnn.com/2012/10/24/pf/college/public-college-tuition/

Part B:

            The article I chose to read was Poverty and Inequality, in Charts by Jared Bernstein of the New York Times, and an advisor to Vice President Joe Biden. As a whole the article delves deep into the workings of poverty in the United States from the early and late 1970s until the present day. One graph examines the percentage of the poor in the United States with the year. I believe it does not display a functional relationship.

            Graph 1.2 does not demonstrate a functional relationship because of the following reasons

                        1. It fails to pass the vertical line test. If a vertical line was placed on Graph 1.2 it would fit. This demotes it from the ability to be a functional relationship.

                        2. Also the outcomes are limited to students with in-state tuition, therefore displaying that these lines could have multiple outcomes if applied properly in the real world.

                        3. Also there are similar outcomes for the same year. This is demonstrated in the graph by how many of the points align perfectly on the graph, showing they are too similar to be part of a functional relationship.

It is true that graph 1.2 is an accurate display of the change in poverty rates for the United States from 1973-2004, but it is not a functional relationship. The relationship in the graph has too many possible outcomes and fails the vertical line test, which means that it cannot be a functional relationship.

Graph 1.2 – Percentage of Poor in the US 1973-2004

Article link: http://economix.blogs.nytimes.com/2014/01/13/poverty-and-inequality-in-charts/?ref=economy