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.
Yu, part B is a great example of a relationship that is not a function because it would not pass the vertical line test. I agree 100%
ReplyDeleteI agree with Alex, using the vertical lines test is one of the best ways to see if the relationship, because there are no exceptions.
ReplyDeleteYu, I agree with you that part A is a function because one input only match with one output.
ReplyDeleteYour example in part B is an excellent choice of a relationship that does not pass the vertical line test and other the other associated tests, and thus is not a function. Interesting data aswell! Well done!
ReplyDeletefish,
ReplyDeleteyour first example is well done and a good topic. the only thing missing in your explanation is to represent the relationship using function notation.
your second example will only work if you take out the time variable and specify that either boston is the input and dc is output or visa versa. otherwise, you have an example in which you have two relationships that are functions of time. you did not clearly specify which of the cities you were to use as output and input.
professor little