Part a:
The article I chose laid out the United States’ debt each year since 1976 in a table. It would considered a function because each input (or independent variable), the year has exactly one output (or dependent variable), the debt. In words; you could say that Y, the year is a function of d, debt. A second way would be d equals “f of Y.” This table would not be considered a linear function, because the average rate of change doesn’t represent the usual pattern of the graph. The function of notation of this table would be d = f(Y), and it is not a mathematical model because the debt doesn’t depend on the year. What year it is doesn’t make the debt.
Part b:
The article for an example of something not a function talks about age, height and weight and their correlations. In oder for something not to be a function, an output can’t have more then one input. For this example, the relationship between age and height wouldn’t be a function because the output, or height, could have more then one input, or age. This happens when people the same age are different heights.
Matthew Small
I like how you explained why the article from part A was a function. It was very clear and easy to follow.
ReplyDeleteI found the debt during each presidents term very interesting. I agree that this is a function because the year has exactly one output. I agree that it is not a mathematical model as the debt has no dependency on what year it is but rather the actions of the current president at the time as well as the overall state of the economy. What other factors do you think there could be that have an impact on the national debt? war?
ReplyDeletematthew,
ReplyDeleteyour first example is a great one and you explained your reasoning for why it is a function very concisely.
in your second example, i like the article, however, you have reversed the criteria for what does not constitute a function. if any input has more than one output, then we do not have a function. what you said was the opposite. otherwise, nice job.
professor little