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

  • Written by Mike Harwood
  • . A step by step tutorial with examples and detailed solutions to graph linear 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.
  • . Tutorial on graphing and sketching cube root 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.
  • . 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.
  • - 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.
  • , 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.
  • . 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.
  • . 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.
  • . 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.
  • . 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.
  • .

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.