Laura Romero Post #2 What is your function?

Part A.
1.  The Washington Post
2.  A function is a relationship where each input has exactly one output. It can be tested with the vertical line test. If a vertical line is drawn through the graph at any point, it should not touch it in more than one point.
3

Bitcoin price fall over three months

Bitcoin price as tracked via the CoinDesk Bitcoin Price Index.

586.76

0

200

400

600

Jul 06

13

20

27

Aug 03

10

17

24

31

Sep 07

14

21

28

Oct 05

586.76

Aug 04 - 12:00 AM

Source: CoinDesk

The Washington Post.            4.  This chart shows the Bitcoin price changes in the last few months. For every point in time, there is a different price for the Bitcoin stocks. There is one output per input.
5. This function is not linear, because the ARC (average rate of change)  is not constant throughout the graph. Bitcoin's stock prices are not stable. This can be seen in the line of the graph which has no pattern of growth or decay.
6. Lastly, the function is not a mathematical model because the output (price of Bitcoin) is not affected by input (time), or vice-versa.

Part B.
1. A relationship is not a function when there is more than one input per output.
2. The Washington Post

3. This relationship shows that as the years pass, and countries develop more, their development slows down, and the change in the patterns of economic growth of emerging markets.

4. This relationship is not a function because there is more than one output per input. Every year, there are different figures for growth, and different countries coupled in the same graph.

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Blog #2

 Part A
1. My function represents the relationship between time and the price of gold.
2.This is a function because for every input there is one output. 
3. http://www.infomine.com/investment/metal-prices/gold/5-year/

4.The graph represents the relationship between the price of gold and the time in months and years since January 2009.
5. The function is not a linear function.
7. As shown in the graph, the ARC is not constant, and without even calculate it we can identify it from the shape of the line which fluctuates over the time period.
8. The function is a mathematical model. because the output is closely related to the value of the input. So for example, the global economic situation the last couple of years have resulted in a drop in the price of gold

Part B
1.http://www.pro-football-reference.com/players/M/MannPe00.htm
2. The relationship between the passing yards of Payton Manning and time is not a function.
3. This relationship is how many passing yards Payton Manning had over his career.
4. It is not a function because P.Manning had the same numbers for passing yards in more than one season, which in our case means that there were more outputs for every input.

Part C

Blog Entry #2

Part A

1.    http://www.nejm.org/doi/full/10.1056/NEJMoa1400506#t=articleResults

The above link is to a very thorough description of all the statistics. The link below is a concise summary of the study.

http://www.healthline.com/health-news/free-contraception-lowers-teen-pregnancy-rates-100114#2

And below is a link to the national pregnancy statistics I used to compliment the study:

http://www.hhs.gov/ash/oah/adolescent-health-topics/reproductive-health/teen-pregnancy/trends.html#.VDR4QYCwLuU

2.    A function is a type of relation where each output has exactly one input.

3.    US National Pregnancy Rates in Teens 15-19

2008	41.5
2009	37.9
2010	34.3
2011	31.3

4.    The relationship shows declining pregnancy rates in teenagers from 2008 to 2011.

5.    No, the function is not linear.

6.    I know the function is not linear because when you take the rate of change, or slope, it is not the same for each set of data. From 2008 to 2009, the ARC is -3.6. However, from 2010 to 2011, the ARC is -3.

7.    The function is not a mathematical model because the pregnancy rate is not dependent on the year. Because of this, you cannot come up with a function notation equation ( f(x)= ). There is no way to predict the pregnancy rate in a given year.

Part B

1.    A relationship is not a function when one output has multiple inputs.

2.    http://www.economist.com/news/finance-and-economics/21618913-after-sharp-slowdown-stimulus-back-agenda-test-will

The link above is for a report on the decline of China’s economy.

3.    I’m not too well read on economic reports, but there are three functions to look at: property sales, investment, and industrial production. They’re graphed over a period of time (x axis), in changing percentages from 2009 to 2014. So this shows the relationship between time and the percentage of change in the Chinese economy.

4.    This relationship is not a function because it would pass the vertical line test. There is not enough information to make a table, because we don’t have exact coordinates, but just looking at it you can see that there are multiple outputs for the different years. 

Nathalie Aissi's Blog Post #2

Part a:

1)   - http://www.runnersworld.com/general-interest/how-fast-could-usain-bolt-run-a-marathon

-My article talks about the different marathoner’s/meter runner’s world records on how fast they could run (time). But I simply chose to focus on Patrick Makau’s different times for the half marathon, 10,000 meters, 5,000 meters, 1 mile and 100 meter times. (Patrick Makau set the men’s marathon world record of 2:03:38 in 2011 in Berlin).

2)   For a function to exist, there must be one output for every input. Also, if graphed, the graph must pass the vertical line test.

3)    

Time (x)	1:01:49	29:18:03	14:39:01	4:42:93	17.58
Distance (y)	21,097 meters	10,000 meters	5,000 meters	1,609 meters	100 meters

4)   This table represents the recorded times Patrick Makau ran in the multiple races represented in meters.

5)    

Calculation	ROC
10,000-21,097/29-60	358
5,000-10000/14-29	333
1,609-5,000/4-14	339
100-1,609/.17-4	394

This function is not a linear function because the ROC’s I calculated at different intervals are not the exact same (constant). 

       7) Like I had explained in problem #5, the function is not a linear function   because when calculating the average rate of change at different intervals, they all came out to be different numbers, which means that the function is not linear and if graphed, the graph would not result in a straight line.

8) This is definitely not a mathematical model because the distance ran by Patrick Makau does not depend on the time he received.

Function notation:  Distance=f(time) ßOutput is always a function of input.

Part b:

1)   Graph has to pass the vertical line test. One output for every input must be present.

2)   http://www.medicalnewstoday.com/info/obesity/how-much-should-i-weigh.php

3)   (This table below is for women of ages 25-59 years)

Height (women)	Weights of women with small frame size
4’10”	102-111
4’11”	103-113
5’0”	104-115
5’1”	106-118
5’2”	108-121

This table above is of various heights of women in ages between 25-59 and the weight they should be between since they are women of small frame.

4) This relationship is not a function because each height in the table has various weights for the small frame women. In a function, there must be one output for every input. In this case, there are is more than one output available for just one input; more than one weight for every height. Also, if this table was graphed, it would not pass the vertical line test for the fact that there are many choices of output, when there should only be one output for every height(input). This shows that this example/table is not a function.

Blog # 2

Asma Aljarbou

Blog  # 2

Math-160

10/7/14

(A)

1.     Find an online periodical (newspaper, journal, magazine), not a math periodical, economics!

My answer is illustrating the relationship between the student’s number of absence and the student’s class grade “I created this example”.

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

For any relationship to be a function, for every input value we should have exactly one output.

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

Student Number of absence     X	Student Class grade  Y
0	100
1	95
2	90
3	85

4.     Explain in words the meaning of this relationship

This relationship shows how the amount of student absence (input) affects his/her class grade (output).

5.     Determine whether the function is a linear function

This relationship is a linear function because the average rate of change between any two intervals is the same, which is equal to 5. And the equation for this function going to be Y = 100 - 5 X. As shown in the graph between the x-axis “Student Number of absence” and the y-axis “Student Class grade ” there is strong linear function created.

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).

The graph shows a perfect linear function, but to be sure we have to compare the ROC for many intervals. For this example the average rate of change in different unites is the same; ROC=100-95/0-1=5, ROC=95-90/1-2=5 and ROC=90-85/2-3=5. For that, it is a linear function.

7.     Determine whether the function is a mathematical model.

This function is a mathematical model because there is a strong relationship between the number of absence and student class grade “X has huge effect on Y”. And the dependent variables rely strongly on the independent variables. And it shows that the more a student miss classes the more he or she affect their grade negatively and result in low grade and having bad grade is because student may miss many classes. And the proper function notation for this example would be Y= F(x).

(B)

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

 “I create this example” between the number of hours a person weekly do and the number of weight loss. 

                                      

2.     Explain in words the meaning of this relationship.

This table shows the relationship between hours of exercise weekly (independent variable) and weight loss (dependent variable). It may represent a mathematical model because of the strong relationship between independent and dependent variable, but it does not represent a function!

Hours of exercise weekly X	Weight loss Kilos Y
0	0
7	4
3	1
5	2
3	3

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

This relationship is not a function because we have the same value of input for different output values; when X=3 we have Y=1 and Y=3 and that against the definition of the function.