The California Mathematics Content Standards -Grade8 9 10 11 12 

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Algebra II

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Standard 24. Students solve problems involving functional concepts such as composition, inverse, and arithmetic operations on functions.

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Skills (Note: none listed for science standards)

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Teacher Strategy An example of the composition of functions might include the combination of discounts one might get using sale prices and employee discounts or money-off coupons.Ask students for additional examples of combined impacts.

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Student Tasks or Scientific Investigation/Experimentation

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Assessment or Scientific Application/Assessment Describe composite functions in functional notation f(g(x)),and give at least two examples and their real-world applications.  Explain how to determine the inverse of a function.Give an example with your explanation.

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Resources and Technology Resources:Algebra Experiments II:Exploring Nonlinear Functions,Addison-Wesley.The Language of Functions and Graphs,Shell Center for Mathematical Education. The “World of Functions ” unit from fourth year textbook of the Interactive Mathematics Program ™ ((IMP ™)deals with all of Standard #24 concepts.Contact Key Curriculum Press at 1-800-995-MATH for ordering information. Chapter One of the Harvard Calculus book also deals with functions. Technology:Tangible Math:Algebra Animator by LOGAL software,Inc.for 7th-12th grade is rated “Desirable ” by the California Instructional Technology Clearinghouse. (Floppy disk,Macintosh,Windows)Students may examine one-to-one and many-to-one functions;compare and contrast motion defined by a constant,linear,quadratic, cubic,rational,exponential,and logarithmic functions.It is an excellent tool to teach graphing skills,compare various graphs, prepare tables,find points of intersections, and connect graphing and equations to real- life situations and word problems.(This software also supports Standards #13,#15, and #25.)

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This page is taken from the Santa Clara Office of Education.

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