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


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Verify graphically or in tables that one function is the inverse of another.

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 paper folding to determine the mirror image.
  • Use the horizontal line test to determine if a function has an inverse that is a function.

    Image of graph and paragraph about in a function every x has one unique y.
  • Use a table to determine if the x and y values are inverses of each other.

    Tables with data for x and y values and inverses of each other.
Representation:
  • Understand the following concepts and vocabulary: domain, range, inverse, function, input, output, graph coefficient, slope, reflect, reflection, mirror image.
  • Understand that for a function, every domain (x) value there is only one range (y) value.
  • Understand that the inverse function creates a mirror image of the original function.

    graph of a inverse function as mirror image to the original function.
  • Understand that the domain (x) and range (y) values of the original function are opposites of each other in the inverse function.
    Data charts of data for x and y and graph with inverses.
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Number: MAFS.912.F-BF.2.AP.4c 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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