What's your function?

Second Blog Post

Marisa Ewing

Part A:

Changes in the DOW Over the Past Six Months

This graph is a representation of the total points in the DOW over the past 6 months (Aug 2014- Present). It is not a liner function because it does not have a constant rate of change. It is not a mathematical model because the output in this scenario is not dependent on input.

Part B:

This is a graph representing the age and height of multiple young boys. It is not a function because there are some inputs that have multiple outputs. Because of that, it also fails to pass the vertical line test, further proving that it is not a function.

Blog Post 2: What's your function? Eamon Martin

Eamon Martin

02-09-15

Blog #2: What’s Your Function?

Part A:

1.      My article is http://www.npr.org/blogs/thetwo-way/2015/01/26/381639118/2015-will-continue-streak-of-shrinking-u-s-budget-deficit

2.      A relationship is a function if a certain number of one area, variable, etc is paired with exactly one number of another.  It is not a function if it does not pass the vertical line rule, in which one value corresponds with more than one value of another variable.

3.       

4.      This graph actually displays two functions, showing the relationship between the year and the United States Federal government revenues, and the year and the United States Federal Government expenditures. 

5.      Neither are linear functions because the values of the expenditures and revenues do not increased by a fixed amount for each year that passes.

6.      It is fairly easy to prove that these graphs do not display a linear function by looking at the rate of change in different time intervals.  Between (approximately) 2008 and 2009, there was a sharp increase in spending, as seen by a steep slope in the outlay graph.  After this period however, the graph shows a negative slope as expenditures (as percentage of GDP) fell.  The rate of change in both time frames is very different.

In 2008 and 2009, revenues fell sharply as well, which can be seen with the negative slope that the graph has in that time interval.  From 2012 however, revenues increased fairly significantly, which can be seen in the positive slope on the graph.  In each, the average rate of change is significantly different.

7.      Both Revenue and Expenditures, as percentages of GDP, can be considered functions of time (year), and thus it is a mathematical model because we can use functional notation to express the relationship.

F(y)= R (for Revenue as percentage of GDP)

F(y)= E (for Expenditures as percentage of GDP)

Part B:

1.      A relationship is not a function if there is more than one output value corresponds with one input value.  This is related to the Vertical Line Test, in which a relationship is not a function if there is more than one Y value that corresponds with a single x value.

2.      *I couldn’t find a periodical that featured a relationship that wasn't a function, so I found a survey done by this website:

3.      The relationship displayed here is that of the connection between height and weight, and the connection they have.

4.      This relationship is not a function because it fails the vertical line test.  As the height of 46/47 inches, there is different weight value and a vertical line can be formed between them.  Thus, it is only a relationship, and not a function.

C. G. What's Your Function?

Channing Gatewood
Professor Little
Applied PreCalculus
8 February 2015

What's Your Function? Blog Post #2

http://www.washingtonpost.com/news/energy-environment/wp/2015/01/23/sorry-skeptics-nasa-and-noaa-were-right-about-the-2014-temperature-record/

(For the above image, I will focus on the table to the left). The above table was taken from the Washington Post, and shows the National Oceanic and Atmospheric Administration's predictions for the relationship between year and percentage probability of that year being the warmest year in history thus far. This table represents a function because for every output (the percentage), there is exactly one input (year). The function is not linear, however, because there is no average rate of change (or slope). The percentages do not change at consistent intervals. The function can be considered a mathematical model, however, because as the years pass, the probability of that year being warmest increases. Therefore, the year in time does affect the probability of that specific year being the warmest.





http://www.economist.com/news/briefing/21640316-children-rich-and-powerful-are-increasingly-well-suited-earning-wealth-and-power

The above graph, taken from the Economist, displays the relationship between SAT scores and family income. This graph does not represent a function because each SAT score range has multiple values (accounting for Reading, Math, and Writing scores), and each output (or income level) has multiple inputs (SAT score categories).

Blog Post 2: What's Your Function: Aroob Qutub

Part A:

-http://www.tradingeconomics.com/united-states/gdp-growth

-A vertical line test could be done to determine wether a relationship is a function, and also a relationship must have one output for each input.

Graph of GDP growth rate in the United States from 2012-2015

- This graph represents the growth rate of The Gross Domestic Product (GDP) in the United States from 2012 to 2015.

-This graph is proved to be a function, because each input is paired with one output, so each year shows a different growth rate. This relation passes the Vertical line test, because there are no vertical lines that intersect the graph at more than one point.

-The relation has both dependent variables the (year) and (GDP growth rate), and the average rate of change between the years isn't constant and the graph isn't a straight line, therefore this relation does not account to be a linear function.

-The function can not be a mathematical model because the (GDP growth rate) depends on economic activity and not on the (year).

Kira Feldmesser #2

Part a:

http://search.proquest.com/docview/227989914/TextPlusGraphics/$N/0?accountid=8285

The function in this study describes the relationship between the willingness to pay for a certain price of potatoes and the number of important qualitative reasons that people are more willing or less willing to buy. Willingness to pay (WTP) is a function of the quantified qualitative reasons one might or might not buy potatoes multiplied by how important the reasons are, plus the normally distributed data gathered in this specific study when the mean is 0 and the standard deviation σ. 

This study is far too subjective and singular to make the function linear, as the amount of importance people place on their respective values when it comes to buying potatoes is going to be vastly different between points based on this small data set. Because ß is multiplied by the input values, I can assume that ß represents the rate of change of the equation, and because it will not be regular, the function is non-linear.

This function is a mathematical model though, because the inputs have a great impact on the outputs, more than just recalling a year or another period of time. 

Part b:

http://delivery.acm.org/10.1145/330000/320440/p9-chen.pdf?ip=147.9.222.63&id=320440&acc=ACTIVE%20SERVICE&key=4E7DC79309562578%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35&CFID=625152959&CFTOKEN=21289195&__acm__=1423455987_0004d8b7ccc216c4e8f403028ed3504d

This is a relationship between people's perceptions of entities and the number of things they imagine. It is not a function because the same input will have multiple outputs and there will be several overlapping data sets. It will therefore fail the vertical line test and be deemed not a function.

What's Your Function: Brenna Carse

Graph of Crude Oil Prices From 2004-2014 (Source: NASDAQ)

Part A:

• This graph represents the prices of crude oil over the past ten years.
• This relationship is a function because each input is paired with exactly one output (each year only lists one price).  This graph passes the vertical line test.
• This function is not a linear function because the average rate of change between points is not constant.
• This function is not a mathematical model because the price of crude oil is not dependent upon the year.

Graph of SPP scores and % of Economically Disadvantaged Students 

Part B:

• This graph displays the relationship between the percentage of economically disadvantaged students in certain schools in Pennsylvania and their corresponding School Performance Profile score in the 2012-2013 school year. (Source: Pennsylvania School Performance Profile) 
• This relationship is not a function because the input values correspond to more than one output value.  This relationship does not pass the vertical line test.  

What's your function?----Yu Daiqing (Fish)

What’s your function? -------------Yu Daiqing (Fish)

Part a:

1.I found an online weather report about the average precipitation in Washington, DC. Here is the link about the report: http://www.weather-and-climate.com/average-monthly-Rainfall-Temperature-Sunshine-inches,Washington-DC,United-States-of-America

2. From the data it shows, I think this relationship

3.

Month, t	1	2	3	4	5	6	7	8	9	10	11	12
Precipitation, P (inches)	3.2	3.1	3.6	3.3	3.9	3.8	4.1	4.2	3.5	3.4	3.3	3.3

4. This is the average monthly precipitation at Washington, DC. T, represents the month, T=1 means January. The precipitation is the function of month. So, it can be represent in function notation as P=f(t).

5.R.O.C=3.1-3.2/2-1=-0.1         R.O.C=3.6-3.1/3-2=0.5        R.O.C=3.3-3.6/4-3=-0.3

7. This function is not a linear function, since it didn’t have the constant rate of change, instead the rate of change are being negative through positive. In addition, we can see from the rate of change, since it was not constant number, so the graph can’t be the straight line. But the linear function’s graph is a straight line.

8. Yes, it is a mathematical model, from the function notation P=f(t), as we can see, the out put is depend on the input.

Part b:

1.The weather report between Washington, DC and Boston. The precipitation between DC and Boston are not functions.

2.

Month, t	1	2	3	4	5	6	7	8	9	10	11	12
Precipitation, P (inches) in Washington (WP)	3.2	3.1	3.6	3.3	3.9	3.8	4.1	4.2	3.5	3.4	3.3	3.3
Precipitation, P (inches) in Boston (BP)	3.7	3.8	3.9	3.6	3.2	3.1	2.9	3.2	3.1	3.4	4.1	4.0

3.This is the average precipitation between two cities, one is Washington, DC, the other is Boston. T represents the month, t=1 means January, and in that month, DC’s precipitation is 3.2 inches and Boston’s precipitation is 3.7 inches.

4. BP is not a function of  WP. For example, when WP=3.3, means in April, November and December, the average precipitation is 3.3 inches. However, in Boston, April is 3.6 inches, November is 4.1 inches and December is 4.0 inches. Since the WP values has correspond to more than one BP value, so that the BP is not the function of WP. A function need to be one output per input.