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MAFS.912.F-BF.2.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Functions: Building Functions
Cluster: Level 2: Basic Application of Skills & Concepts
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.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

TEST ITEM SPECIFICATIONS

  • Item Type(s): This benchmark may be assessed using: TI item(s)

  • Assessment Limits :
    Functions represented algebraically are limited to linear, quadratic, or
    exponential.

    Functions represented using tables or graphs are not limited to linear,
    quadratic, or exponential.

    Functions may be represented using tables or graphs.

    Functions may have closed domains.

    Functions may be discontinuous.

    Items should have a single transformation.

  • Calculator :

    Neutral

  • Clarification :
    Students will determine the value of k when given a graph of the
    function and its transformation.

    Students will identify differences and similarities between a function
    and its transformation.

    Students will identify a graph of a function given a graph or a table of
    a transformation and the type of transformation that is represented.

    Students will graph by applying a given transformation to a function.

    Students will identify ordered pairs of a transformed graph.

    Students will complete a table for a transformed function. 

  • Stimulus Attributes :

    Items should be given in a mathematical context.


    Items must use function notation.


    Items may present a function using an equation, a table of values, or

    a graph.
  • Response Attributes :
    Items may require the student to explain or justify a transformation
    that has been applied to a function.

    Items may require the student to explain how a graph is affected by a
    value of k.

    Items may require the student to find the value of k.

    Items may require the student to complete a table of values.

SAMPLE TEST ITEMS (1)

  • Test Item #: Sample Item 1
  • Question:

    The table below shows the values for the function y = f(x).

    Complete the table for the function begin mathsize 12px style y equals f left parenthesis 1 fifth x right parenthesis end style

  • Difficulty: N/A
  • Type: TI: Table Item