EMMA WALL Blog Post 2: Conjunction Junction, Whats your function

4.     Explain in words the meaning of this relationship.

Cince the year 1978, the ice extent is decreasing. It is a function because there is one x for every y. 

5.     Determine whether the function is a linear function. 

The trend line is a linear function

6.     If the function is linear, explain in detail how you know the function is linear (be sure to refer to the average rate of change). 

Because a trend line is drawn, it is the average rate of change over time, meaning the decreasing rate of change is linear.

8.     Determine whether the function is a mathematical model (be sure to use function notation.)

The function is a mathematical model because it is composed of relationships and variables which constitute a function.

Part b:

1.   .

2NOT A FUNCTION

3.     Explain in words the meaning of this relationship.

This compares the price of a Big Mac to whether an average citizen can afford said Big Mac. 

4.     Explain in detail how you know the relationship is not a function.

This does not qualify as a function because it fails the vertical line test, therefore, there is not one x for every y.

http://www.nytimes.com/2012/09/16/opinion/sunday/do-tax-cuts-lead-to-economic-growth.html?_r=0


This is an article that was published two months prior to the Romney-Obama presidential election.  The article goes into the positive and negative effects of tax breaks for the wealthy.  Above is a graph displaying the economic growth of the US over the last 20 or so years.  In the timeline, periodical tax breaks are shown displaying their effectivity.  This graph is not linear or exponential because the growth and decline is totally sporadic.

Blog #2 Kate Cornman

Kate Cornman Blog Post #2

Part A:
1. This graph on commodity-price indexes was taken from an article from the Economist on January 9th, 2014. The article describes the concerns whether the Chinese "super cycle" is running off and not improving its growth.
2. The relationship of a function is that there is exactly one output per input. A function also is determined by passing a Vertical Line Test.
4. The graph specifically shows how between 1845 to present day the overall trend of commody price indexes in industrials has decreased.
5. This is not a linear function.
6. The average rate of change is not consistent so it is not linear. For example at one point, (85-50)/ (1850-1840)=3.5 versus another R.O.C. on the graph which is (125-85) /1870-1860=4.
7. Since a mathematical model is supposed to help predict future events through an equation, this graph does not represent a mathematical model because it could not predict what will happen the next year.






Part B:
3 & 4.) This article is from the Economist describing job growth in poor countries by income group. This graph is NOT a function because there are multiple outputs with each input. The relationship in this graph is that the middle and working class are increasing as well as jobs in the countries represented on the graph.

http://www.economist.com/blogs/graphicdetail/2014/01/daily-chart-11

My Function

Part A: 

Real Madrid's goals for 2013-2014 in the last 6 months: 

August (1)                                 2 Golas
September (2)                          5 Goals 
October    (3)                          4 Goals 
November   (4)                       4 Goals 
December   (5)                       2 Goals 
January         (6)                      3 Goals    

Every input has exact one output, and that's a function. It's not a linear functions because the rate of change is different and not the same. 

(5 - 2) / (9 - 8) = 3

(4 - 5) / (10 - 9) = -1 
* The rate of change is not the same then its not liner function. 

I don't think it's a mathematical function because the team performance is not depending on the time of the year. Real Madrid like any team will always try to score more goals no matter what time of the year. 

Part B: 

If the input doesn't have one exact output we can say this relationship is not function. Relationship is function when every input has one exact output. Example for a relationship is not a function: 


 
It's not a function because 5 in X  has 3 different values in Y, and (4,3) in X  has no value in Y.  

http://espnfc.com/team/stats/_/id/86/league/esp.1/real-madrid?cc=4716

Blog Post #2

Part A:

So for this weeks' blog post I decided to pull a graph from an article that discusses the relationship between innovation and the percentage of employment seen in the United States. Now, although the article discusses innovation and unemployment, the author felt it was first necessary to provide a larger more broad view of job retention over the years in specific sectors of the job market as seen below: 

Now if we recall the lecture in class we know that functions will only have one output per the input given. If we take a look at any of the information provided we will see that for each sector they are in fact functions, since for each year we are only provided with one percentage of employment. As for whether or not they are linear we would rely on the secondary test, or otherwise known as the vertical line test. By simply viewing these graphs they would appear to pass the vertical line test, however I will also have to run with the assumption that the graphs follow the integrity of a single percentage per year as suggested in the title. With all of the graphs successfully passing the vertical line test, we are finally left to see if they are in fact linear, and to do so we must see if there is a constant average rate of change. Although we are unable to attain the accurate numbers to test for the constant rate of change from the picture, if we rely on intuition and by the overall trends of the lines we will know that they do not in fact have a constant rate, seeing as employment fluctuates on yearly basis and can be affected by external factors. Therefore, although they appear to be linear they do not pass all three test and would be considered a non linear function. All of the functions are representative of a mathematical model because the outputs or percentage (dependent variable) are reliant on the inputs or year (dependent variable) leaving us with: f(percentage)=year.

Part B:

The second chart that I managed to discover was a break down of the oscar nominations for each film that is up for the best picture of 2014. We know this is certainly not a function because for each of the movies we are seeing multiple outputs. We are presented with both the total number of nominations but for each input we will also have the number of previous nominations that the directors or actors have received. Therefore it cannot be a function. 

Blog Post #2

This periodical displays China's GDP growth over a 13 year period. There is a relationship between GDP growth in percent and years from 2000. The relationship presented in this periodical does not represent a linear function, because the rate of change is not constant. This graph represents a mathematical model because each input has exactly one output. 

The graph above does not represent a function because the average rate of change is not constant. The slope of part S, U and W are all equal to zero. 

Rebecca Hernandez's Blog 2

Part A:

http://www.economist.com/blogs/freeexchange/2013/04/decoupling

I chose the periodical the economist and the article titled Decoupling: One Expensive Euro. The relationship between functions and non functions is that functions have one input per output and non functions do not. The function is a non-linear function and I know that it is not linear because the function it passes the vertical line test. The function is a mathematical model because the input is dependent on the output. 

Part B: 

http://krugman.blogs.nytimes.com/2013/08/28/the-asian-crisis-versus-the-euro-crisis/

The relationships in these is not a function because the input and output are not related. When a relationship is not a function the input and output are not dependent and it does not pass the vertical line test. 

Blog Post #2

Part A

This is a function, the relationship is that one output exists for every input, and it passes the vertical line test.
It is linear because it passes the V.L.T. and has an average rate of change that can be calculated
It is a mathematical model because a domain and range can be calculated
D [93,13]
R [0,7]

Part B
 This is not a function, there are two outputs for every input. Spending is being calculated by digital spending and non-digitial (the two outputs)
Because of the two outputs this is definitely not a function

Blog 2

Part a:
The criteria for determining whether a relationship is a function is if there is only one output to each input and that it passes the vertical line test.
I went on The Economist and found an article about house mortgages and there was a graph that showed the relationship between house mortgages of houses that exceed the home value and years.  The function is not linear because the rate of change is inconsistent.  The function is not a mathematical model because the mortgages of house does not depend on the year.

Part b:
the criteria for a relationship that is not a function is if there is more than one output to each input.
I read another article on The Economist about skills that are most helpful in different countries.  The chart I used is not a function because there are more than one output to each input.  This graph shows the relationship between countries and the usefulness of numeracy skills.

Blog Post 2--Dawson

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.

4. This relationship represents a process where an input is manipulated through the function to become one output. This allows us to view relationships between the variables. In this case it demonstrates different years's (with recession periods marked) unemployment levels, allowing us to analyze long term unemployment.
 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.

Blog #2

The graph I chose was from CNN and it shows China's total government spending since 2009. This relationship shows the national spending over time. This is a linear function. This function is linear because there is only one amount of dollars for every year. The second article I found contained a relationship that wasn't a function was also from CNN. This article compared the minimum wage every year in different states. This relationship means that there are different wages in one year. This is not a function because there are more than exactly one point for every year.

My function is...

1-      Sources : http://www.forbes.com/sites/scottmendelson/2014/01/07/box-office-benchmarks-catching-fire-to-pass-iron-man-3-frozen-to-top-300m/

And 

        http://www.boxofficemojo.com/weekend/chart/?view=main&yr=2014&wknd=02&p=.htm

2-      I was going through the weekly gross total for movies the other day. So, I chose the top 5 out of the whole list - only the Name of each movie for Tuesday 1/14 and Wednesday 1/15 Gross. The relationship is a function because each movie I have on the list has its own gross:

Name of the movie	Tuesday 1/14	Wednesday 1/15
1-      Lone Survivor	$3,623,025	$2,817,500
2-      AMERICAN HUSTLE	$1,306,965	$1,011,962
3-      THE WOLF OF WALL STREET	$1,293,865	$1,000,355
4-      Frozen	$976,359	$751,353
5-      AUGUST: OSAGE COUNTY	$824,455	$700,110

                                             

3-

  

4-      Relationship of this function between the top 5 movies and their gross for two days in a row. The input is the name of the movie that people go watch, and the output is how much money that specific movie made that day.

                                          (Movie)= f(TotalGross)

5-      The function is not linear because if I calculate the change in movies’ gross and dividing it by the time, I won’t get equal results. 

delta D1 / delta T1    is not equal to  delta D2 / delta T2

6-      I see the function as a mathematical model because the output (gross) depends on the input (movie).

B)

http://blogs.computerworld.com/it-careers/21993/women-computer-science-visual-trendline

I found this interesting article about women majoring in computer science through time.

At the beginning while reading I thought of it as a function until the numbers became percentages and weren’t mentioned at the end. The article became statistical rather than functional.

For example, when the writer starts with 1986 having an exact number of 15,129 female in IT field is different than mentioning just a percentage for 2004 of 34% and followed by a dropped percentage of 28% for 2011. I don't think I can have a function of of difference type of data (percentages vs numbers), unless I convert one to the other. Briefly, in this specific article each input (year) has multiple output (number that's missing) and a percentage.