Investigating Functions Using Spreadsheets
by Margaret Sinclair |
Why use spreadsheets to investigate functions?
- because spreadsheets allow students to view the numerical representation of a function beside the graphical display;
- because most students have access to spreadsheet software.
When students are introduced to linear relations in grade 9, solve quadratic equations in grade 10, and study exponential behaviour in grade 12 they often don't identify connections between different function types. Each equation has its own mysterious parameters. The behaviour of each graph is learned in isolation.
Through the following investigations, students work with a variety of functions, altering parameters and observing the changes in the numerical data and in the graphical representation. They then are asked to analyse the results, and to form conclusions about functions in general.
Setting up Data and Plot windows
The spreadsheets in this unit were created using Microsoft Excel 5.0. They can be accessed and used onscreen once your browser has been set up to use Excel as a Helper Application. If you do not have Excel, please see alternate instructions for setting up the activities.
Lessons
In the first part of this unit students explore the effects of altering parameter values in a variety of function equations:
m in the equation y = mx
b in the equation y = mx + b
a, p and q in the equation y = a(x-p)^{2}+q
a and n in the equation y = ax^{n}They examine the results in both the numerical data and the graph and predict what changes will cause the graph to pass through particular points.
- Access each spreadsheet and follow the instructions within.
Each sheet should have 3 windows - a table window, a plot window and an instruction window. If one is missing, use the UNHIDE command under the Window menu to view all three.
It may help, after reading the instructions, to close one window and enlarge the others. NOTE: Altering the spreadsheet, or saving it, will not affect the original!
If you have any problems, please access the printable copy at Sample Lesson Spreadsheets.
- Answer the questions under each topic.
Linear Functions I y = mx Question Set 1 Linear Functions II y = mx+b Question Set 2 Introduction to Power Functions y = ax^{n} Question Set 3 Quadratic Functions y = a(x-p)^{2}+q Question Set 4
Seminars
In the second part of the unit, students, in pairs, choose to examine the role of the parameters in one of the following, and present their results to the class:
a, b and k in quadratics written as y = ax^{2}+bx+k
n and k in polynomial functions of the form y = x^{n}+k
a, p and k in absolute value functions of the form y = a[abs(x-p)]+k
a and b in exponential functions of the form y = ab^{x}
a and k in rational functions of the form y = a/x+k
a and k in the root function ax^{1/2}+k
- Choose a function to investigate and access the spreadsheet.
- Based on your experiments in changing parameter values, formulate rules that can help you predict function behaviour.
Quadratic Function - standard form y = ax^{2}+bx+k Polynomial Function y = ax^{n}+k Rational Function y = a/x + k Square Root Function y = ax^{1/2}+k Absolute Value Function y = a[abs(x-p)]+k Exponential Function y = ab^{x}
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