Part a:
According to the Charlottesville, VA police department property crime in Charlottesville for the most part has been decreasing since 2010. http://www.charlottesville.org/index.aspx?page=257 (click on the 5 year YTD comparison graph). This graph is a function because each x value has a different y value. The graph although it spikes passes the vertical line test.
The rate of change from 2010 to 2011 was -106 meaning that as time increased crime decreased by 106. However, there was a spike in 2012 by +47 meaning that as time increased crime increased again by 40. In 2013, the rate of change fell to -14, meaning as time increased crime decreased by 14.
This would not be a linear function because the average rate of change fluctuates between positive an negative.
This would not be a mathematical model because the is not dependent on the input.
Part b:
When comparing statistics of weather, by looking at the weather trends of one day and taking out the year the graph is no longer a function because there will be multiple outputs for one input. http://www.wunderground.com/history/airport/KDCA/2014/1/17/DailyHistory.html?req_city=Washington&req_state=DC&req_statename=District+of+Columbia shows the weather history of January 17th weather, because there is no official year for this information and it all applies to January 17th, it is not a function when graphed.
I like how you chose a crime related topic because it really showed the function relationship well! I also thought it was clever how you chose to do weather for your non-function example; it worked very well and the reasoning was clear.
ReplyDeleteChoosing weather for your example of a situation that isn't a function was a really good idea since it's such clear example of it.
ReplyDeleteVery easy to understand your examples and the information that comes with it!
ReplyDeleteariana,
ReplyDeleteyour first example is a very good one, and relevant! i know people who live in charlottesville. you did a excellent job of explaining why the relationship is a function and identifying the inputs and outputs.
your second example, however, has some issues. it is true that there are relationships, but you would need to specify which relationship you are looking at. for instance, wind speeds for that day or pollen count or something. in any case, however, any of these relationships would still constitute a function as you wouldn’t be able to have two different wind speeds at the same time during the day.
professor little