Part
A - Function
Online, using The Economist, I was able to find an
article investigating the West’s impact on Russia’s economy. The article
contained the below graph, which shows a function representing the declining
value of roubles (Russia’s currency) due to the invasion of Russia by large
western companies.
In this graph the
vertical axis represents the value of roubles per dollar (v) and the horizontal axis represents the month in the year 2014 (m). So, this function would be written
as f (v) = m if put into function notation.
We can tell that this graph is in fact a function because it passes the
vertical line test, and each input has exactly one output. However, this
function is not a linear function. There is no constant rate of change and the
graph doesn’t show us a straight line. The average rate of change would need to
be a constant one for this graph to be linear. It is also not a mathematical
model because the value of one rouble does not at all depend upon the month or
year.
Part
B – Not A Function
Using
the online annual report of the California Commission on Health and Safety and
Workers’ Compensation (CHSWC) I was able to find the below graph, which
represents the comparison between the permanent disability benefit level and
the benefit value (from 1984 to 2001). That being said, this graph is basically
comparing between disability benefit level and benefit value, also showing how
they have changed over the years.
In
order to see whether or not this is a function, we must first recall that
functions pass vertical line tests and that in a function each input has
exactly one output. Here, however, the only input giving the same output each
time is the first input. After the first, all the following inputs give two
different outputs. This violates the rules of a function, and therefore proves
that the below graph does not represent a function.
So I can see why the Rouble has been going down for the past few months. It really correlates with the amount of craziness that has been going on with them and their government. With the way that they're going, the Rouble is going to be even more worthless....
ReplyDeleteIt seems like it would be so hard to tell if graph number 1 really passes the vertical line test. All the points are so close together. I really like the second example its cool that you show it through a bar graph.
ReplyDeletehi, emma rose!
ReplyDeletei really like your first example. you did a great job of explaining the article generally and mathematically. and good job of using function notation! as i've mentioned in several other blog posts, it would have been nice, however, to see calculations for ROC to confirm your explanations about linearity.
your second example actually shows two relationships that are each separate functions, so this does not qualify as a NON function.
prof little