This sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

PRESCRIBED LEARNING OUTCOMES

It is expected that students will perform, analyse and create transformations of functions and relations that are described by equations or graphs.

It is expected that students will:

• describe how various translations of functions affect graphs and their related equations:

• describe how various stretches of functions (compressions and expansions) affect graphs and their related equations:

• describe how reflections of functions in both axes and in the line affect graphs and their related equations:

• using the graph and/or the equation of describe and sketch
• using the graph and/or the equation of describe and sketch
• describe and perform single transformations and combinations of transformations on functions and relations

SUGGESTED INSTRUCTIONAL STRATEGIES

The transformation of functions helps to develop students’ visualization skills and spatial sense. Practice in this area will help students answer questions about "how much" and "where" in other areas of mathematics. It will also help in the understanding of functions as a precursor to calculus.

• As transformations of functions are applicable for all functions studied in this course, review these with students whenever a new function is introduced.
• Students can use appropriate technology (e.g., graphing calculator, computer software) to investigate transformations. On the same coordinate plane, they could graph:
  
  Have them sketch each transformation on grid paper using the "trace" or "table" feature for accuracy. The first transformation (e.g., compression/expansion) might always be in red, the second reflection step always blue and the final translated function always in green, with the original basic function sketched accurately in pencil. Have students analyse the changes in the original graph as the equation is modified, and repeat this process for other transformations.
• Have students use the parabola or circle to play "function calisthenics". Ask students to model changes to functions using their body position in relation to others.

SUGGESTED ASSESSMENT STRATEGIES

Transforming functions requires both an understanding of algorithms and a developed spatial sense. Assessment strategies should focus on both abstract and concrete transformation skills.

Question

• To check students’ understanding of quadratic functions and relations, circulate through the classroom and note:
  • the extent to which students can analyse a particular quadratic relation given a graphing analysis outline
  • whether students can recognize the declining characteristics (locus) and properties of each type of quadratic relation, and can relate the type of conic to specific equations
  • whether students can explain the effect of an x2 term in an equation — how does it affect the possible values of x (domain)? What about y2?

Collect

• Have students compile portfolios containing examples of their work modeling each basic type of relation studied. Ask them to give examples and explain how various transformations can be applied to each type. Assess portfolios with students for completeness, variety, organization, accuracy, presentation, and for specific criteria sets.
• Have students graph the transformations of the basic equations manually. Look for their abilities to draw the graphs with paper and pencil, without the use of a graphing calculator.

Self-Assessment

• Based on a previously developed, student-generated checklist of graphing criteria, students could summarize analyses of their own work by listing what they do well and where they need to improve.

RECOMMENDED LEARNING RESOURCES

Multi-Media

• Mathematics 12, Western Canadian Edition
  Ch. 1 (Sections 1.1 - 1.6)
  Ch. 4 (Section 4.7)
  Ch. 9 (Sections 9.4 - 9.5)
• MATHPOWER 12, Western Edition
  Ch. 1 (Sections 1.1, 1.3, 1.4, 1.6)

Software

• Secondary Math Lab Toolkit
• ZAP-A-GRAPH

Games/Manipulatives

• String Invision Conics Model

© 2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: December 4, 2000

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