Colorado State University Algebra Discussion

This week, your task is to create a relation involving two variables from your daily life, and then discuss whether or not your relation is a function.

Your task for this discussion is as follows:

1. Fill in the table with what you are typically doing during each of the following times.

1. Represent your relation (T, A) in an alternative manner other than the table created in part (a). (i.e., as ordered pairs or with a mapping diagram.)
2. Determine whether or not your relation is a function. Why or why not?
3. In your responses to peers, comment on whether or not you think their relations are also functions.(see attached peers)

Here is my list of everyday activities. Judging from this schedule, I need to
get out more!
Time (t)
Activity (A)
4AM
Sleeping
8AM
12PM
Working
Eating
Lunch
Working
Studying
Sleeping
4PM
8PM
12AM
This table can also be represented as a set of ordered pairs as follows, given
that time (t) is the input (independent) and activity (A) is the output
(dependent):
{(4AM, Sleeping), (8AM, Working), (12PM, Eating Lunch), (
Mapped out in a diagram, it is also clear to see that each input (t) has one
output (A):
4 AM
Sleeping
SAM
Working
12 PM
Eating Lunch
4PM
Studying
В РМ
12 AM
Based on the Abramson (2015, Section 3.1) definition of a function where
each input has exactly one output, this relation is a function which
represents Activity as a function of Time. It can be written as A = f(t).
Conversely, since there are more than one of the same output (sleeping and
working) that can be mapped back to different times, then this is not a one-
to-one function. Likewise, if Activity was the input and Time was the
output, then the relation would not be a function because there would be
multiple outputs for one or more of the inputs.
The following table represents the time slots for my activities.
Time (T) Activity (A)
4 AM Sleeping
8 AM
Working
12 PM
Eating
4 PM
Working
8 PM
Eating
12 PM Sleeping
As you can see the activities revolve around sleeping, eating, and working
which is productive but a bit of an eye opener. The independent variable in
this situation is Time (T) and the dependent variable is Activity (A). As seen
below the input and outputs can be illustrated in a diagram.
activas a
HAN
Sleeping
BAM
12 PM
60
Work
4 PM
SIM
12 AM
We can also view this as order pairs as seen below.
{(4 AM, SLEEPING), (8 AM, WORK).(12 PM EATING),
Based on the diagram, you can easily see that each independent variable
has exactly one output. It is stated by Abramson (2015), “A function is a
relation in which each possible input value leads to exactly one output
value.” This verifies that this is indeed a function because it follows the
definition of a function. Therefor the function would be represented by
A= f(T). You can take it a step further and say that it is not a one-to-
one function because the outputs correspond to more than one input.
Cievabani