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.