Standard 3 : Create new functions from existing functions.



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General Information

Number: MA.912.F.3
Title: Create new functions from existing functions.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Functions

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.F.3.1: Given a mathematical or real-world context, combine two functions, limited to linear and quadratic, using arithmetic operations. When appropriate, include domain restrictions for the new function.
Clarifications:
Clarification 1: Instruction includes representing domain restrictions with inequality notation, interval notation or set-builder notation.

Clarification 2: Within the Algebra 1 Honors course, notations for domain and range are limited to inequality and set-builder.

MA.912.F.3.2: Given a mathematical or real-world context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations. When appropriate, include domain restrictions for the new function.
Clarifications:
Clarification 1: Instruction includes representing domain restrictions with inequality notation, interval notation or set-builder notation.

Clarification 2: Within the Mathematics for Data and Financial Literacy course, problem types focus on money and business.

MA.912.F.3.3: Solve mathematical and real-world problems involving functions that have been combined using arithmetic operations.
MA.912.F.3.4: Represent the composition of two functions algebraically or in a table. Determine the domain and range of the composite function.
MA.912.F.3.5: Solve mathematical and real-world problems involving composite functions.
MA.912.F.3.6: Determine whether an inverse function exists by analyzing tables, graphs and equations.
MA.912.F.3.7: Represent the inverse of a function algebraically, graphically or in a table. Use composition of functions to verify that one function is the inverse of the other.
Clarifications:
Clarification 1: Instruction includes the understanding that a logarithmic function is the inverse of an exponential function.
MA.912.F.3.8: Produce an invertible function from a non-invertible function by restricting the domain.
MA.912.F.3.9: Solve mathematical and real-world problems involving inverse functions.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MA.912.F.3.AP.2: Given a mathematical and/or real-world context, combine two or more functions, limited to linear, quadratic, and polynomial, using arithmetic operations of addition, subtraction, or multiplication.
MA.912.F.3.AP.4: Given a composite function within a mathematical or real-world context, identify the domain and range of the composite function.
MA.912.F.3.AP.6: Determine whether an inverse function exists by analyzing graphs and equations.
MA.912.F.3.AP.7: Represent the inverse of a function algebraically. Use composition of functions to verify that one function is the inverse of the other.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Formative Assessments

Name Description
Furniture Purchase:

Students are asked to write two explicit functions given verbal descriptions in a real-world context, compose the two functions, and explain the meaning in context.

How Much Bacteria?:

Students are asked to write and combine an exponential and a constant function from a verbal description to use when answering a related context question.