Relations and Functions Project: A Question of Time

A relation is a set of ordered pairs. When both sets are numerical, it is possible to graph the relation. When it is possible to graph the relation, we can analyse the trends in the data visually – say what is the maximum value, the minimum value, when the values are increasing, decreasing, staying steady and so on.

Example: The height of a capsule on the London eye Ferris Wheel, t minutes after boarding.

The purpose of this project is to become familiar with the vocabulary and concepts used in math when discussing relations, and to become familiar with graphing on geogebra or on desmos.

Get Started!

Open a Google Doc and put a title on four pages:

Page 1: Title of project, Author (you), Date (today) and Introduction

Page 2: Data Set

Page 3: Graph

Page 4 Discussion of data set and graph

 

Choose, find and/or generate a data set

The first step is to decide what numerical relationship to graph. For the purpose of this project, we will use data that changes over time. You just need to think of something that changes over time that you have some familiarity with. Here are some ideas:

  1. What percentage of the moon is illuminated by the sun each day in the month of [April]?
  2. What is the temperature of coffee taken every minute after making the coffee for 20 minutes?
  3. What is my heart rate taken once a minute during a 30 minute workout?
  4. What is the population of this area according to census data over the last … years?
  5. What was the highest temperature in this area recorded in each of the past 30 days?
  6. Price of gasoline recorded once every 7 days over the past year.
  7. Time of sunrise in [city] recorded once a week over one year.
  8. Distance from home during any one 24 hour period during the last week.
  9. Number of [Canadian] athletes in the winter games from 1924 – 2018
  10. Amount of data used in MB during each billing period for your phone over the last 12 months.

Record the data on a Google Sheet. The first column should be time – possibly minutes, days, months or years. Time can be an awkward quantity, (not base 10, months are not of equal length etc) so ask if you have questions on how to record the time. The second column should be your data values. Copy paste the table onto page 2 of your Google doc.

Graphing

Import your data to a desmos file or to a geogebra file, and plot on the graph as you wish.

To graph, you need to:

Open a table (desmos) or spreadsheet view (geogebra)

Copy and paste your data from your google sheet to desmos/geogebra

Figure out how to label each axes with the correct measurement (eg, Time) and the unit (eg Time (years)).

Change the max and the min on the x and the y axes so that you can view all of your data points.

Save your work.

You may if you wish join your points up, if there is some sense to that.

Copy to clipboard so that you can paste it onto page 3 of your google doc.

Discussion:

The final page. Your discussion should include

A statement regarding which of your two variables is dependent on the other. (When does the sun rise? It depends on the time of year…).

The time period – the domain of the relation you graphed (starts …., ends….)

The minimum value of your data points, the maximum value of your data points, whether or not if you collect data again you might get other values. This is the range of your relation.

A discussion of the trend of the relation – over time, does your values increase/decrease/remain constant – is there ever a sharp increase or decrease? etc.  Write your comments in context (eg, the temperature of the coffee decreases sharply between … and …, rather than ‘the graph decreases sharply). You can be verbose here.

A ‘rate of change‘ at some point in your graph. ‘over the year/day/hour/minute …., the data changed by ….’.

Conclude with any other observations on the data set that are easily perceived by the graphical representation of the numbers.


Next page: Graphing Relations on the Cartesian Plane

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