Blog Post #2

Part A:
https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOMyzNvh0JGFLNupqBX94hCzxJGE4SS5FcVCisv-lOn2L5GpWW8kHw0Q1Krfa0Wg1vblZV_c4zxT5xuWdapBL1XsJqrsP7BN5NNeaTwwlPp8DivU4eUd3Ob3i_jsvk7iduUBYIYnF_rG_V/s1600/its-getting-better-infant-mortality-rates.jpg

1. As the years go on, the infant mortality rates decrease.
2. The relationship is indeed a linear function.
3. It passes the vertical line test and for each year there is a value on the graph (for each input there is one output).
4. The function here, D=f(Y), is a mathematical model because the trend of the infant mortality rates decreasing steadily as the years progress are in direct relationship with each other (due to advancements in technology and such).

Part B:
http://wattsupwiththat.files.wordpress.com/2013/01/surfacetemps_japan3.png

1. This graph demonstrates the relationship between temperature anomalies over the years.
2. This relationship is not a function because there are not inputs matched for every output value and this graph does not pass the vertical line test.

Blog 2 Functions

Part a:

http://themcgowangroup.com/wp-content/uploads/chart-12.png

1.       As Years increase average GDP growth changes

2.       The relationship is a Function

3.       This chart is a function because it passes the vertical line test and each year (input) leads to a single output.

4.       The function G=f(Y) is not a mathematical model as it does not follow a trend because the year does not result in a specific GDP figure.

Part b:

1.        http://blog.chron.com/climateabyss/files/2011/08/txsummno11-600x463.gif

It shows the relationship between average temperatures and total rainfalls.

2.       It is not a function since many of the inputs do not equal single outputs, and it as such does not pass the vertical line test. (The trend line is not relevant to this relationship in this sense.)

What’s Your Function?

Blog submission number 2

Due Date: September 9, 2012 by 11:59 pm Eastern Standard Time

Point value: (15 points)

Learning objectives:

• Recognize, observe, formulate, and understand mathematical connections that functions and their graphs have in everyday life
• Analyze, think critically about, and demonstrate a meaningful understanding of various mathematical functions and their graphs by effectively communicating their thinking and reasoning for their solutions and mathematical connections to real world situations (in other words, rather than simply knowing how to solve any particular problem, students should be able to explain how they to come to a particular solution and as well as explain why it is correct)
• Apply general strategies to more than one type of graph, function, or equation 
• Comfortably and effectively utilize a variety of strategies to solve any given mathematical problem involving functions and their graphs

Background:

This blog submission is an exercise in recognizing real world applications of a mathematical concept.

Directions:

Part a:

1. The Washington Post
2. Every input has exactly one output and passes vertical line test
3. The graph is showing how the population of New Mexico is approaching zero.
4. Not linear
5. The function is not linear because it is not a straight line. An equation cannot be created because there is no exact output for every input. 
6. The graph is not a mathematical model because the population does not depend on the time. The outputs do not depend on the inputs. 

http://www.washingtonpost.com/blogs/govbeat/wp/2014/01/17/population-growth-in-new-mexico-is-approaching-zero-and-other-bad-signs/

Part b:

1. The Washington Post
2. The graph shows how we have begun to use less and less energy to produce a given unit of economic activity. Mostly caused by fuel-efficient trucks, more efficient power plants, and any other energy-efficient manufacturing techniques.
3. The graph does not pass the vertical line test.

http://www.washingtonpost.com/blogs/wonkblog/wp/2014/01/17/can-we-sever-the-link-between-energy-and-growth/

Part c:

1. After completing your blog entry, thoughtfully and critically comment on the posts of members in your blog group. 

Getting to know you

(Blog submission number 1)

(10 points)

Learning objectives:

By the end of this course, students will be able to do the following…

• Recognize, observe, formulate, and understand mathematical connections in everyday life
• Thoughtfully apply mathematical concepts to real world situations  
• Recognize evidence of the many mathematical concepts that are at work in real life situations  
• Analyze, think critically about, and demonstrate a meaningful understanding of mathematical concepts by effectively communicating their thinking and reasoning for their solutions and mathematical connections to real world situations (in other words, rather than simply knowing how to solve any particular problem, students should be able to explain how they to come to a particular solution and explain why it is correct)
• Apply general strategies to more than one type of problem  
• Comfortably and effectively utilize a variety of strategies to solve any given mathematical problem 

Background:

A couple of the primary focuses for this class greatly center on your ability to effectively communicate mathematical ideas and to collaborate with members in your classroom community.  As a result, for this class, you will be required to create and maintain a mathematics blog.  The purpose of this blog will be for you to gain experience effectively communicating your mathematics understanding as well as collaborating with your members of your classroom community about mathematical concepts.  Some submissions will require that you respond critically to topics in class, from lecture, or from textbook readings.  Some submissions will require that you do research on a topic related to concepts discussed in class, elaborate on them, explain them in real world language, and apply them to real world situations.  

You will be required to submit six blog entries.  In addition to submitting your own work, you will be required to make thoughtful comments on posts from members in your learning community. Your submissions will be graded using a rubric with categories for creativity, problem solving, thoughtful reflections, insightful comments, etc.    

In many classes, especially math classes, learning is rarely extended beyond the hour and fifteen minutes of lecture time.  Hence, another purpose for this blog is to help prevent a stagnant learning environment and support and encourage learning beyond the classroom walls.  My goal is for you to become a part of a community of learners…learning, teaching, and supporting one another, as well as developing the skills you need for your own learning.

Directions:

Part a:

1. Once you receive an invite from me, go to the following url http://findingfunctionality3.blogspot.com/and subscribe to the class blog.
2. Once you have created your profile, answer the following questions and post them to the class blog.  (you may number your answers, answer the questions in narrative form, I’m not going to be picky for your 1^st submission)
3. Students who submit the questionnaire by 11:59pm, Monday, January 13, will receive two extra credit points added to the first quiz.  (you may number your answers if you like or answer the questions in narrative form… whatever you prefer.)
4. The purpose of this questionnaire is to get to know you a little bit better and also to learn things that can assist in guiding my instruction of the class this semester.  Thank you! 

Questions:

1. What is your full name?

Camila Augspurg

1. Do you have a nickname that you prefer to go by?

Cami

1. What is your height in inches?

5’ 5”

1. What is your age in years?

18

1. What time do you generally wake up on any given day?

10 am

1. What is your favorite candy?

Crunch

1. What is your favorite snack food?

Grapes

1. Who is your favorite musical artist/band?

Alt - J

1. Do you have any hobbies/things you like to do for fun?

Listening to music, watching shows and movies, spending time with friends and family

1. What is your mathematical background? (Not limited to the list below…list other topics if needed)

Precalc Honors and Calculus

1. Which mathematical concepts in this class do you think you may struggle with/what are your math weaknesses/fears?

Word problems

What is your comfort level with any of the following algebraic topics? 

Write one of the following next to each topic:

Very comfortable (V) comfortable (C)     uncomfortable (U) extremely uncomfortable (E)

Equations C

Factoring V

Adding/subtracting/multiplying/dividing fractions/rational expressions C

Simplifying expressions V

Operations on roots and fractional exponent expressions U

Operations involving whole number exponent expressions U

Finding common denominators V

Inequalities C

Functions C

Absolute value V

Linear functions U

Systems of equations C

Domain and range V

Inverse functions U

Transformations (shifting, scaling, stretching, etc) C

Quadratic functions C

Completing the square C

Exponential functions C

Logarithmic functions V

Base e U

Graphing V

Trigonometric concepts C

1. Which mathematical concepts covered in this class do you think you will excel in/what are your strengths/where are you confident?

1. Which social media formats are you familiar with? 

Texting facebook pinterest flickr wordpress blogspot tumblr twitter google plus

1. Which social media formats do you use most frequently?

Texting facebook pinterest Instagram

1. What is your major?

Graphic Design

1. Why are you taking this math class?

Required

1. Will you take other math classes in the future at American University or will this be your only math class? If yes, which classes will you take?

Yes, I am thinking in having a double major with Marketing, so any mathclass that is required. 

1. What do you hope to learn in this class?
2. Is there anything else you would like me to know about you?

Part b:

1. After completing your blog entry, comment on at least two of your classmates blog submissions (you are free to comment on more than two posts if you like).

Blog 2 Dave Sweet

Part A:



2. A function exists if a graph shows a relationship between the x value and the y value, and passes the vertical line test (meaning there is never more than one output per input.

3. The functional relationship here is between family income (i) and student test scores (t). t = f(i).

4. As family income increases, test scores also increase.

5, 6, 7. The graph is not linear because the rate of change is not constant.

8. Yes, because there is a consistent positive change after every x value.

Part B: 

1. A function does not exist if there is more than one Y value per X value. 

2. 


3. This graph is not a function because a vertical line passes through three separate points.

Graphics and functions, Blog post 2

1a) This function represented in a graph shows the correlation between total population in an area and the number of people living under the poverty line. Every district area has one image dependent solely on the number of people under the poverty line in comparison to the total local population. This function is not a linear function because the rate of change is not on a constant growth or loss curve. This is a mathematical model because the outcome, the percentage of people living under the poverty line is dependent on the input the population.
http://www.nytimes.com/newsgraphics/2014/01/05/poverty-map/?ref=multimedia


1b) Here the relation between the deliberation time and the verdict is not a function because the outcome the verdict does not depend on the time spend on the deliberation. Although the relation between the deliberation and therefore the time taken to reach a verdict is a significant relation, there is neither an input nor an output in this scenario.
http://www.usatoday.com/story/news/nation/2014/01/17/ricin-georgia-guilty/4592157/

Part a:

1.

X (years)	Y (net income)
2004	389
2005	494
2006	564
2007	673
2008	316
2009	392
2010	948

Data can be found using the link: http://www.gurufocus.com/financials/SBUX

This table shows the net income of Starbucks corporation over 6 years. 

1.     Recall the criteria for determining relationships that are functions.

          This is a function because each value has exactly one output, and passes the vertical line test.

2.     Search the periodical for a relationship that represents a function (in graph, table, or formula format).

          This table represents a function because all values have exactly one output.

3.     Explain in words the meaning of this relationship.

          Over the years, the graph shows how the net income of Starbucks corporation increases and decreases over time.

4.     Determine whether the function is a linear function.

         This function not a linear function because values increase and decrease inconsistently over the years making the graph more jagged. 

5.     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).

          The function is not linear.

6.     If the function is not linear, explain in detail how you know it is not linear (be sure to refer to the average rate of change).

          The graph is not linear because the rate of change in between points is not the same each time; therefore the points cannot be connected by the rate of change.

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

         The graph is not a mathematical model because values are not dependent on one another.

 Part b:

1.     Recall the criteria determining relationships that are not functions.]

A relationship cannot be a function if multiple outputs for one input.

2.     Find an online periodical with a relationship that is not a function.

http://www.erh.noaa.gov/

      On this site, I compared the data from March and April and the values have repeating outputs for one input.

3.     Explain in words the meaning of this relationship.

      This data shows the average amount of Snowfall in Dulles over time.

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

      This relationship is not a function because it has repeating output values, and does not pass the vertical line test. 

Blog 2--Relationships of Iron Man Yearly Circulation

Part A: 
A relationship is a function if an input value does not contain more than one output value. In other words, there is one output for one input. When dealing with a graph, it is easy to identify a function if the graph passes the vertical line test, in which a vertical line does not touch more than one point on the graph.

With that in mind, Comichron is a website which tracks the sales figures of popular comic books. In this example, Comichron has compiled the Average Paid Circulation (or the total paid circulation) of all of the Invincible Iron Man comics sold between 1980 and 2004. The values can be found at this link and are highlighted in yellow:
http://www.comichron.com/titlespotlights/ironman.html

In this relationship, the input is time in years (1980 to 2004) and the output is the total paid circulation of Iron Man comics in that year. Therefore, Total paid Circulation (C)=f(year).

This relationship is not linear. The figures cannot be connected by a consistent rate of change. For example, from 1995-2000 the values are:

The Invincible Iron Man paid circulation:

Year: 1995--82,469
         1996--64,717
         1997--184,386
         1998--151,476
         1999--92,008
         2000--69,257

There is no linear slope.

This relationship is, however, a mathematical model. The output (the average paid circulation) is dependent on the input (year) since the APC could not be calculated without the duration of the input (year).

Part B: 

For part B, I am going to use the same example as Part A. However, I will change my output from the total paid circulation to total circulation. This will then include the total PAID circulation (highlighted in yellow), the total FREE circulation and the combined circulation. Thus, this relationship is no longer a function. Relationships are not functions if one input has multiple outputs. Using each form of circulation (outputs) of all Iron Man comics in relation to one year (input) gives the input 3 distinctive outputs--Paid circulation, Free circulation and Total circulation. Therefore, since the input (year) now has three outputs instead of one, the relationship is not a function.

Blog #2 - Sam Lichtenstein

Part a:

1. The Human Security Report is an online periodical that compiles data on various aspects of global human security issues.

2. A relationship is a function if each input has exactly one output. Graphically, a relationship is a function if it passes the vertical line test.

3. http://www.hsrgroup.org/docs/Publications/HSR2005/Figures/2005HSReport-fig5_4-War-Poverty-Association.pdf

4. This relationship illustrates how the probability of conflict in a state decreases as that state's GDP per capita rises.

5. The function is not linear, and instead looks somewhat like a geometrical progression.

6./7. The function is not linear because the average rate of change drastically changes once GDP per capita rises above about $2000.

8. This function is not a mathematical model because other circumstances could trigger conflict in a state besides its poverty levels. Also, the government could be rich while every citizen is very poor, causing a low GDP per capita, but with the rich government hogging all resources. Thus, these outputs, the probability of conflict, are not entirely dependent on the GDP per capita.

Part b:

1. A relationship is not a function when it involves inputs with more than one output.

2. http://www.nytimes.com/2014/01/18/us/as-californias-drought-deepens-a-sense-of-dread-grows.html?ref=us

3. This article shows the relationship between the passage of time and the amount of land with severe to exceptional drought in California.

4. This is not a function because each year, or input, has many outputs, as the percentage of land changes throughout the year.

Blog Post #2

Charlie Krampf 

Blog Post #2

http://www.economist.com/blogs/graphicdetail/2014/01/daily-chart-9 

This is a chart of some of the most popular movies that have come out recently. They rang from a group of people falling into the earths atmosphere, “Gravity” to a man falling in love with a computer, “Her”. 

There is a direct correlation between the ticket sales and how many nominations the movie was given. The formula for this would be, R (revenue) = F (N). N being Nominations. 

There is one input for every output. 

Work Sheet Answer

The correlation between the decrease in VCR sales and the decrease in DVD sales are very similar. This is because all these devices are in the same industry, and are just a more technologically advanced version of the prior. When the DVD player was introduced, the consumer market was very intrigued because it was a brand new device to them. This is why VCR sales dropped so quickly and the DVD excelled so quickly. When the Blu-Ray player was introduced into the consumer market, there was probably less of an interest, because it was pretty much the same thing as a DVD player, just a better picture resolution. From personal experience I really can’t tell the difference from a DVD or Blu-Ray picture. My family still has yet, to catch onto the Blu-Ray trend. The Blu-Ray player will most likely become as common as the DVD player, but it will not happen as quickly as the DVD player took over the VCR. 

Blog Post #2- Caitlyn McMUnn

1. The graph that I found relates how many years of education one has and how much the average salary is per years of education.

2. In order to be a function, every input must have exactly one input

3. The graph can be found with the link provided below:
http://soc101.wordpress.com/2006/10/28/education-pays-income-by-education-level/

4. By looking at the graph, one can infer that the more education a person, the higher their salary will be

5. No, the function is not linear

7. I determined this because the rate of change between the points were not the same

8. The function is a mathematical model, because the amount of time you put into your education has a direct correlation with how much money you are going to earn in your career

Part B:

3. Students' ages and heights would be a good example of something that would not be a function

4. I know that this would not be a function because there can be more than one height for each age, and vice verse. If the input has more than one output, then it is no longer a function. Visually, I could use the vertical line test to see if it passes as a function or not.

Jan 17 Nina Ferguson

Part 1.

1. This graph is the relationship between the annual income from before, during, and after the recession in the US. This graph depicts the household income of times after the recession. The household demographics give people a better visual of how much the recession effected different house incomes.

2. This is not a liner function because it does not make a straight line on the coordinate plane. The graph goes up and down inconsistently, which would not be the case if it were a linear equation. 

3. This function is a mathematical model, because the outputs are dependent on the inputs. From looking at the graph, the income rates of dollars are dependent on the years of when it happened. The function notation of this would be (Y) for years, which is the input and (I) for income which is the output. I = f(Y) 

Part 2. 

This is not a function because the relationship between the lines do not depend on each other. This graph fails the vertical line test, therefore is not linear. The input and the output of this graph (which are 1, 1 and -1, 1) do not depend on each other and that is one of the biggest factors of the overall function. 

Blog post 2

Part A

1.)

The graph above shows a function in an article about how the human population has increased over time. It is a function because it passes the vertical line test and every input has an output. It is not a linear function because there is no constant rate of change considering population increases more rapidly as time goes on. It isn’t a mathematical model since the outputs aren’t dependent on the inputs or in function notation, Q isn't’t dependent on t.

Part B

1.)    The article I found discusses how education correlates to unemployment rate; however, neither column represents a function because if graphed both will fail the vertical line test. Instead of being a function, this table just compares the unemployment rate to those with less than high school education and those who have a college education or more. 

Blog 2 Ale Mathies

What’s Your Function?

Blog submission number 2

Due Date: September 9, 2012 by 11:59 pm Eastern Standard Time

Point value: (15 points)

Learning objectives:

·         Recognize, observe, formulate, and understand mathematical connections that functions and their graphs have in everyday life

·         Analyze, think critically about, and demonstrate a meaningful understanding of various mathematical functions and their graphs by effectively communicating their thinking and reasoning for their solutions and mathematical connections to real world situations (in other words, rather than simply knowing how to solve any particular problem, students should be able to explain how they to come to a particular solution and as well as explain why it is correct)

·         Apply general strategies to more than one type of graph, function, or equation

·         Comfortably and effectively utilize a variety of strategies to solve any given mathematical problem involving functions and their graphs

Background:

This blog submission is an exercise in recognizing real world applications of a mathematical concept.

Directions:

Part a:

1.       BBC

2.       Has to pass vertical line test, every input has an output.

3.       Graph on weather http://www.bbc.co.uk/weather/5128581

4.       This is a graph of the weather. It gives you the month for time and the temperature in Centigrade.

5.       This is not a linear function.

6.       This is not a linear function because it is not a straight line. We can’t just write a formula for this graph because there is no equal relation between the points.

7.       The function is not a mathematical model because the outputs are not dependent on the inputs.

Part b:

1.       The criteria for determining relationships that are not functions are that they do not pass the vertical line test, not every input has one output, functions cannot have multiple outputs for one input.

2.       This relationship that is not a function talks about the Iowa caucus. It is not a function because this relationship depends on the population on the given area. (Taken from CNN) http://cnnpressroom.blogs.cnn.com/2012/01/03/cnn-uses-studio-technology-to-explain-iowa-caucus-2/?iref=allsearch