a.
1. This is from an article in the economist talking about long term joblessness in the United States. This graph that was posted in the article relates the year with unemployment numbers.
http://www.economist.com/news/united-states/21592624-can-american-labour-policies-face-challenge-long-term-joblessness-long-time-gone
2. A function can be defined as a relationship that does not have multiple outputs per x inputs.
3.
This graph can easily be determined to be a function by the vertical line test, which this graph passes. While it appears to have a vertical line at first glance at approximately the year 2009, this is actually a rapidly sloping incline. Realistically thinking we can easily tell this is a function because there are not going to be two different unemployment figures for a given year.
5/7 This Function is clearly not linear. Upon quick inspection one can see that it is asymmetrical looking, with quick climbs and sharp dips. From a Mathematical perspective we can tell this is not linear due to inconsistent average rates of change. Formula: (Y2-Y1)/(X2-X1) Take for example from 2,000 to 2,003 the average rate of change is .27 (.5-1.3)/(2000-2003)= .8/3 whereas from 2,009 to 2,011 it is 1.625.
(1-4.25)/(2009-2011)= 3.25/2
8. This function is a mathematical model because it is a mathematical description of a real situation. The situation represented by the graph is the U.S. long term unemployment, and based on the graph it is apparent how the 2009 recession sky rocketed unemployment.
y=f(x)
With y being the unemployment number and x being the year.
b.
1. Something is not a function if it has multiple outputs per inputs.
2. Taken from http://www.cse.unsw.edu.au/~lambert/img/ozcompass.png
3./4. This is a political survey that relates economic views and libertarian vs. authoritarian views through data collected from Australian blogspace. There are multiple outputs for a given input so it is not a function.
This is organized really well and you went into a lot of detail with your answers, it is clear and easy to understand.
ReplyDeleteI agree with Erin it's really organized good job.
ReplyDeleteThis second one looks confusing, and you answered everything in detail. A job well done
ReplyDeleterobbie,
ReplyDeleteyour first example is really good. someone else used this example, as well. your explanations are detailed and mostly correct. your explanation for mathematical model does not follow, as the definition for a mathematical model is a function where outputs are dependent on inputs. i do not believe that is the case here. other than that excellent job on your first example!
for your second example, nice job, as well. students had a harder time finding an example of a non-function, but you pulled it off.
professor little