Part A
1). http://www.statista.com/statistics/265125/total-net-sales-of-apple-since-2004/
1). A relationship is not a function when there are more than one output per an input, and when the relation fails the vertical line test when graphed.
1). http://www.statista.com/statistics/265125/total-net-sales-of-apple-since-2004/
3).
2). A relation is a function when there is exactly one output for every input. To test if a relation is a function, a function must pass the vertical line test.
4). My graph, which represents the Revenue generated by Apple from 2013-2014, is a function because it is a relation where there is exactly one output per input, and when graphed on a coordinate plan, it passes the vertical line test where x, represents years, and y, represents total net sales measured in billions of U.S. dollars.
5). The relation present does not appear to be a liner function due to the fact that there isn't an average rate of change present throughout. Therefore, there is no constant slope for the graph. However, it does pass the vertical line test, so the relation is indeed a function, but not linear.
6). N/A
7). The function is not linear because there is no constant rate of change present throughout. In order to determine the ROC, you choose two points on the graph and then apply the slope/Rate of change formula: y2-y1/x2-x1. Then, after finding the rate of change between two points, you then must determine the ROC between all points on the graph. If the ROC remains consistent throughout, we can know that the function is linear, if the ROC is not consistent, the function is not linear.
8). The function is not a mathematical model because the output being recorded, billions of dollars, is not a function of the input, years.
Part B
1). A relationship is not a function when there are more than one output per an input, and when the relation fails the vertical line test when graphed.
2).http://www.fao.org/docrep/006/ad316e/AD316E02.htm
3.) In this relationship, the height, input, is being compared to age, output. There are more than one outputs per a given input, thus determining that this relation is not a function.
4). I know that this relationship is not a function because the data presents information proving that there is more than one output per a given input in the model. In addition, the data cannot pass the vertical line test when graphed. This makes it mathematically impossible for this relationship to be a function.
You have really good examples of a functions and a non-function, and your explanations are very good as well.
ReplyDeleteI like how you are very detailed in your explanations!
ReplyDeleteYou used great examples that easily show which graphs are functions and which graphs are not.
ReplyDeleteEverything is detailed and well explained
ReplyDeletejohn, nice job on your first example. your explanations are clear and detailed, however, it would have been nice to confirm non-linearity with actual calculations when you were explaining that part. additionally, you were supposed to use function notation when explaining the math model part. other than that, good work.
ReplyDeleteyour second example i was confused at first because i didn't know if you were using the scatter plot or the negative exponential relationship. if you are referring to the scatter plot, then your are correct that it is not a function.
prof little