What's your Function?
AJ Ledesma
Section A
2. A function is a relationship in which there are exactly one output per input. One major requirement for a function is the vertical line test; function can be represented in many ways including a table or a graph.
3.
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| Pumpkin Sales over the past five years. |
4. This graph demonstrates the sales of pumpkins over the past five years. It is suggested that since Starbucks has introduced its Pumpkin Spiced Latte in the past decade, sales of pumpkins have skyrocketed. The y axis is the amount of sales (In Millions) and the x a-xis is the period of time.
5. This graphs passes the vertical line test, which means that there are not two points on the same output. However, this graph does not demonstrate an average rate of change because sales are always changing based on consumers. There is no constant rate at which pumpkins stay steady.
6. Does not apply to this graph.
7. In order for a function to be linear it has to past two major test: the vertical line test and have an average rate of change. This graph does pass the vertical line test however it does not have a constant rate of change. To find the rate of change we must plug in our x values and y values in this formula:
Y2 -Y1 / X2 -X1
There is not constant rate of change when plugging in the values of the graph. When the sale of pumpkin declined from 2010 to 2011.
8. This is not a mathematical model because not all of the sales of Starbucks Pumpkin Spiced Latte relies on the overall sales of the pumpkin industry. Other companies also have been a contriutor of the increase of pumpkin sales. Companies such as Samuel Adams Beer, they have increase pumpkin sales when they introduced their Pumpkin Ale to customers.
Section B
Happiest States in the United States.
1. In order for a relationship not to be a function is when the function DOES NOT pass the vertical line test. There are more than one output per input.
3. This relationship demonstrates the how Americans are happy based on how wealthy they are.
4. I can tell that this graph is NOT a function because there are multiple outputs per one input value. Each blue dot represents how happy one family is and how much their income in. Based on that information one family can make the exact same income as another family.
I really like how you looked for a function that is related to Halloween! The second relationship is very interesting too, particularly because of how it shows that Americans are happier if they are wealthier, which in my opinion is wrong, because money does not buy happiness.
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ReplyDeletei freaking love this post! very creative of you to "october" theme it! your explanations and calculations are great, although i would have added actually SHOWING the ROC calculations for explaining why the function is not linear. also, you forgot to use function notation when explaining whether or not it was a math model.
nice job on your second scatter plot example, too!
prof little
I really enjoyed your blogpost because you made a normal math function a fun experience by relating it to halloween. It was easy to understand and had en interesting topic!
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