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:

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

Time (T) | Activity (A) |

4 AM | |

8 AM | |

12 PM | |

4 PM | |

8 PM | |

12 AM |

- 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.)
- Determine whether or not your relation is a function. Why or why not?
- 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

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