Function Deduction
Grade Level: Grades 11 and 12
Description
Each team will try to identify a series of mathematical functions given the graph with certain key points identified.
Participants
Teams of four to six. All students may participate. Each school may have up to two teams but only one team per school allowed per session.
Procedure
Each team will be seated at a table, and be given an envelope with 17 pages inside ( 15 Main Functions and 2 Bonus Functions). On each page will be an accurate graph of a mathematical function; and, where necessary key points 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.
Judging
Each question will be scored out of 5, so that the maximum team score is 75 marks. Alternate forms of equations are acceptable. In the case of a tie then the time of the teams completion will be taken into account.
Training for the Event
These resources will be helpful as you practise for the competition
- FunctionID. The program plots the graph. You deduce the equation. Written by Mike Harwood
- Graphmatica. You enter the function. The program plots the graph.
- Tutorial on Graphing Functions
- Graphing Linear Functions. A step by step tutorial with examples and detailed solutions to graph linear functions.
- Graphing Square Root Functions. A step by step tutorial on graphing and sketching square root functions. The graph, domain, range of these functions and other properties are discussed.
- Graphing Cube Root Functions. Tutorial on graphing and sketching cube root functions.
- Graphing Quadratic Functions. A step by step tutorial on how to determine the properties of the graph of quadratic functions and graph them. Properties, of these functions, such as domain, range, x and y intercepts, minimum and maximum are thoroughly discussed.
- Graphing Cubic Functions. A step by step tutorial on how to determine the properties of the graph of cubic functions and graph them. Properties, of these functions, such as domain, range, x and y intercepts, zeros and factorization are used to graph this type of functions.
- Graph of Rational Functions - Sketching. How to graph a rational function? A step by step tutorial. The properties such as domain, vertical and horizontal asymptotes of a rational function are also investigated.
- Graph of Sine, a * sin(b x + c), Function. Graphing and sketching sine functions of the form f (x) = a * sin (b x + c); step by step tutorial.
- Graphing Tangent Functions. A step by step tutorial on graphing and sketching tangent functions. The graph, domain, range and vertical asymptotes of these functions and other properties are examined.
- Graphs of Logarithmic Functions. Graphing and sketching logarithmic functions: a step by step tutorial. The properties such as domain, range, vertical asymptotes and intercepts of the graphs of these functions are also examined in detail.
- Graphs of Exponential Functions. Graphing and sketching exponential functions: step by step tutorial. The properties such as domain, range, horizontal asymptotes and intercepts of the graphs of these functions are also examined in detail.
- Graph, Domain and Range of Absolute Value Functions. This is a step by step tutorial on how to graph functions with absolute value. Properties of the graph of these functions such as domain, range, x and y intercepts are also discussed.
- Free graph paper is available.
FAQ
Do the solutions have to be in standard form or expanded? For rational and reciprocal functions, which form does the answer need to be in?
It does not matter. Multiple forms are accepted. For example the quadratic may be in any form.
Are calculators allowed?
Basic calculators can be used. Graphing calculators or programmable calculators are not allowed.
