This bar graph
courtesy of http://www.macworld.com/article/1131754/appleearnings.html. The article that accompanies this graph describes Apple's profit over the years. This data shows revenue in millions of dollars in relation to year. This is a function because we define a function as being a relationship in which there is exactly one input per output. Here there is one revenue output per quarter or per year. This relationship is not linear however because in linear functions the rate of change is constant at every interval. If that were true of this function we would see the revenues increasing steadily over time instead of at different rates per quarter/year. This relationship does not represent a mathematical model because revenue is not dependent on time.
Here the data is shown in a scatterplot courtesy of http://www.governing.com/news/state/gov-biking-walking-cities-obesity-study.html
A function is defined as a relationship in which there is exactly one output per input. This data set does not represent a function because there is more than one input per output (ie. there can be many values of people who are not overweight for the same percentage of commuters who walk or bike).
Hi Taylor, I was thinking about using data from Apple as well, so I am glad to see that someone else used it. As for your answers in Part A, I think you answered each question very well and directly. I would suggest numbering the answers rather than putting it in a paragraph, but that just me. Also my graph in Part B shows almost the same data that mine does (except yours is walking and mine is driving). Looks like great minds think alike!
ReplyDeleteHey Taylor! Like Sarah, I was super glad you used an Apple graph, since I did for mine too, and I was worried I was choosing a rather well known company to illustrate my points, but I think you did a great job analyzing the graph and it's validity for a function. I felt your explaination in Part A regarding the average rate of change could have been stronger, as if I were someone with no math knowledge, I would have no idea what concept you were referencing.
ReplyDeletetaylor,
ReplyDeletereally nice job on both of these examples! i love the biking/walking example that you used for your NON function. the only thing i would add to your first example is to show the ROC calculations to further confirm that the function is not linear, and also you forgot to use function notation in explaining the last part.
other than that, great job!
prof little