Physics and Astronomy

Function Deduction

Each team will try to identify a series of mathematical functions given either a table of values, the graph, or both.

Participants Teams of up to six.
Procedure Each team will have from 4 to 6 members with at least one student from each of grades 11, 12 and OAC. The remaining team members may be from any grade level.

Each team will be seated at a table, and given an envelope with 15 pages inside. On each page will be an accurate graph of a mathematical function; and, where necessary, a table of values for the unknown function. The functions will be in one of six categories: linear, quadratic, polynomial, rational, trigonometric, exponential and logarithmic. In some cases, the category will be given to you. The object of the competition is to identify the equations of the functions within the time limit of 30 minutes.

The team can divide up the work as they see fit and discuss, cross-check, argue and so on as they come to their collective conclusions about the unknown functions.

Training for the Event

A computer program called Identify for PC's running under DOS is available for download. It will allow you to practise your skills in identifying functions from each of the six categories. This program presents the unknown function either as a graph or as a set of numerical values. You can also ask for the values of any point on the graph or trace the curve and get a running tabulation of points on the curve. This information then allows you to establish the equation. You can input the equation when ready and the computer will tell you if it is correct or not. The authors of the program have placed it in the public domain, so that you may make as many copies as you need.

Number of Functions in the Program:

Linear 40
Linear & Quadratic 60
Polynomials 84
Rational 32
Trigonometric 88
Exponentials and Logarithmic 24
A set of bonus questions will be taken directly from some of the more challenging functions in the program.

Training for the Event

Download the DOS based program Identify. It is stored in a self-extracting archive called funcmath.exe.

This public domain program will seem archaic to students who have known only Windows. If anyone designs a more modern substitute and is willing to share it, please contact the web master.

Judging Each question will be scored out of 5, so that the maximum team score is 75 marks. This score will contribute 33.3% to the overall score for the Mathematics Triathlon. The other components of the Triathlon are Lightening Calculators and Serial Series - Serious Stuff.
Source London District Science Olympics. This event was created by Eric Wood.

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