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Slide 1

Function Transformations Unit

For

An Algebra 2 Course

A Project Funded by the National Science Foundation,

and written by Kirk Taylor

Slide 2

Why?

NCTM Standards and California Content Standards call for all students to have skill in function transformations.

Most Algebra 2 curriculums teach it, but not as a cohesive and comprehensive set of principles.

It gives students the power and knowledge to transform many types of functions.

Slide 3

Transform = Change

Graphs are pictures of relationships

Mathematics is a symbolic language of relationships

Slide 4

Teach the rules of FT as a single comprehensive set of principles

Not add time to the Algebra 2 calendar.

Use simple, low-technology and graphing calculators to give students confidence with functions

Slide 5

Students will learn to recognize by shape a group of six function families: Quadratic, Cubic, Absolute Value, Square Root, Exponential and Linear, and to learn the name of a ‘locator point’ for each family.

Students will learn the rules for function transformation, and be able to apply them to all six function families. They will be able to make accurate sketches of functions.

Students will be able to correctly identify to what degree functions have been translated, reflected, and/or stretched/compressed.

Students will increase their fluency with function notation.

Slide 6

More math vocabulary: asymptote, increasing/decreasing function, odd/even function, inflection point, point symmetry, and more.

Better curve-sketching techniques

Establish foundations for further study

Slide 7

Introducing the Big 6:

Quadratic Sketching Techniques

Cubic Generalizing power functions

Absolute Value

Square Root

Exponential

Linear

Slide 8

Work collaboratively under well-defined guidelines

Make conclusions and conjectures based on experiences

The Student’s Role

Slide 9

Guided Inquiry Activities

Set clear rules for collaboration.

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- Goals
- Learning Objectives
- Other Learning Objectives for the FTU
- Unit Overview
- Guided Inquiry Activities
- Assessment
- Teacher Observations
- Assessment Tools

- Factoring Polynomials
- Simplifying Radical Expressions
- Functions and Graphs
- Dividing Polynomials
- Ten Ways of Looking at Real Numbers
- Real Numbers
- Multiply two polynomials using the FOIL method, Box method and the distributive property

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