Blog Post #2

Part A:

So for this weeks' blog post I decided to pull a graph from an article that discusses the relationship between innovation and the percentage of employment seen in the United States. Now, although the article discusses innovation and unemployment, the author felt it was first necessary to provide a larger more broad view of job retention over the years in specific sectors of the job market as seen below: 

Now if we recall the lecture in class we know that functions will only have one output per the input given. If we take a look at any of the information provided we will see that for each sector they are in fact functions, since for each year we are only provided with one percentage of employment. As for whether or not they are linear we would rely on the secondary test, or otherwise known as the vertical line test. By simply viewing these graphs they would appear to pass the vertical line test, however I will also have to run with the assumption that the graphs follow the integrity of a single percentage per year as suggested in the title. With all of the graphs successfully passing the vertical line test, we are finally left to see if they are in fact linear, and to do so we must see if there is a constant average rate of change. Although we are unable to attain the accurate numbers to test for the constant rate of change from the picture, if we rely on intuition and by the overall trends of the lines we will know that they do not in fact have a constant rate, seeing as employment fluctuates on yearly basis and can be affected by external factors. Therefore, although they appear to be linear they do not pass all three test and would be considered a non linear function. All of the functions are representative of a mathematical model because the outputs or percentage (dependent variable) are reliant on the inputs or year (dependent variable) leaving us with: f(percentage)=year.

Part B:

The second chart that I managed to discover was a break down of the oscar nominations for each film that is up for the best picture of 2014. We know this is certainly not a function because for each of the movies we are seeing multiple outputs. We are presented with both the total number of nominations but for each input we will also have the number of previous nominations that the directors or actors have received. Therefore it cannot be a function.