Function Transformations Unit
An Algebra 2 Course
A Project Funded by the National Science Foundation,
and written by Kirk Taylor
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.
Transform = Change
Graphs are pictures of relationships
Mathematics is a symbolic language of relationships
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
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.
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
Introducing the Big 6:
Quadratic Sketching Techniques
Cubic Generalizing power functions
Work collaboratively under well-defined guidelines
Make conclusions and conjectures based on experiences
The Student’s Role
Guided Inquiry Activities
Set clear rules for collaboration.