Access Point #: MAFS.912.F-BF.2.AP.4b (Archived Access Point)


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Write an expression for the inverse of a simple function.

Clarifications:

Essential Understandings

Concrete:

  • Identify a function.
  • Identify the x and y variables.
  • Identify the domain and range of a function.
  • Identify the inverse of a function.

    Image identifying the inverse of a function.
  • Use tools (patty paper, transparencies, mirror, mira, graphing calculator) to reflect the original function.
  • Identify an expression for a given function using manipulatives or a graph.
  • Use this table or template to rewrite the function as its inverse.

    Table of function and inverse definitions and formulas.
Representation:
  • Understand the following concepts and vocabulary: main, range, inverse, function, input, output, graph coefficient, slope, reflect, reflection, mirror image.
  • Understand that the inverse function creates a mirror image of the original function.

    Graph of function and inverse showing mirror image of original function.
  • Understand that the domain (x) and range (y) values of the original function are opposites of each other in the inverse function.

    Chart data and graphs for function and inverse of function.
  • Understand that the inverse function creates a function that uses the inverse operations of the original function.

    Example using the inverse operations of the original function.
    Click Here
  • Write an expression given a graph.
  • Write an expression given a table.
  • Rewrite an equation for a given variable.

Number: MAFS.912.F-BF.2.AP.4b Category: Access Points
Date Adopted or Revised: 06/14 Cluster: Build new functions from existing functions. (Algebra 1 - Additional Cluster) (Algebra 2 - Additional Cluster)

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Related Standards

Name Description
MAFS.912.F-BF.2.4: Find inverse functions.
  1. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x³ or f(x) = (x+1)/(x–1) for x ≠ 1.
  2. Verify by composition that one function is the inverse of another.
  3. Read values of an inverse function from a graph or a table, given that the function has an inverse.
  4. Produce an invertible function from a non-invertible function by restricting the domain.



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