Objective
The objective of this project is to research and graph a function and to build familiarity with the vocabulary and concepts of functions through analysing your function in context.
The relation is the set of ordered pairs – your data set. You are not required to find a formula for your points.
The task
This project has four parts: Choose a data set as your ‘set of ordered pairs’; graph on paper; graph on GeoGebra, analyse the function.
Ideas for a Data Set
The first step is to choose a numerical relationship to graph. For the purpose of this project use data that changes over time. Think of something that changes over time that you have some familiarity with. Here are some ideas:
- The percentage of the moon is illuminated by the sun each day in this month.
- The temperature of coffee taken every minute after making the coffee for 20 minutes.
- Your heart rate recorded once every minute during a 30 minute workout.
- The population of this area according to census data over the last … years.
- The highest temperature in this area recorded in each of the past 30 days (or this day on each of the past 30 years)?
- The price of gasoline recorded once per month over the past few years.
- The time of sunrise in [city] recorded once a week over one year.
- Your distance from home during any one 24 hour period during the last week.
- A height measurement marked on a cupboard wall at home since you were small.
- The number of [Canadian] athletes in the winter games from 1924 – 2024
- The amount of data used in MB or GB during each billing period for your phone over the last 12 months.
Record your data on a Google Sheet or draw a table on paper. The first column should be time – possibly minutes, days, months or years. The second column should be your data values. Check your data set with the teacher before proceeding with the rest of the project.
Function analysis
The analysis of your function should include these details:
Choose a letter for each variable in your relation. State which variable is independent (horizontal axis) and which is dependent (vertical axis).
State the domain of the relation you graphed (starts …., ends….). What does the domain mean in your context?
State the minimum value of your data points and the maximum value. State the range of your relation. What do these numbers mean in your context?
Include 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, for example: “the temperature of the coffee decreases sharply between minutes … and …”, rather than “the graph decreases sharply”.
Write a sentence about the amount of change between data points – does your function increase/decrease uniformly, does it have any sudden steep changes up/down etc.
Conclude with any other observations on the data set that are easily perceived by the graphical representation of the numbers.
An example of anaylsis is provided here: The height of a capsule on the London eye Ferris Wheel.
Suggested Page Structure
| Page 1 | Title page. Your name, the course, the date, a title for your project, a sentence describing the objective of the project and perhaps a relevant image. |
| Page 2 | Data set: Draw a table of your data or copy and paste your data set and state the source of your data. |
| Page 3 | Graph on paper: Use graph paper, decide how to draw your axes, label your axes, plot your points and give the graph a title. |
| Page 4 | Graph on geogebra.org/calculator. Adjust and label your axes, plot your points and use the ‘polyline’ command if you want to join your points. |
| Page 5 | Function analysis. |