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.
"Good linear function! Good correlation between each missed day
ReplyDeleteequals a total of 5% off a students over all grade. I can see why it is a
function!"
I like your examples, as they are very similar in style, and therefore offer great comparison to show liner vs. non-linear functions. It is very good that you showed your calculations for the ROC is order to further prove that it is linear. Good idea to add a graph from outside to show what the line looks like!
ReplyDeleteI like the correlation between the missed classes and the students grades, very interesting! You also give very good supporting evidence for each of your graphs.
ReplyDeleteasma,
ReplyDeletegood self generated examples. i like that you showed ROC calculations when explaining linearity in your first example.
for your second example, it is not a mathematical model. if it is not a function, it cannot be a mathematical model since math models are always functions. other than that, nice job.
professor little