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MAFS.912.F-LE.1.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Functions: Linear, Quadratic, & Exponential Models
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting 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 will be assessed using: OR item(s)
    N/A
  • Assessment Limits :
    Exponential functions represented in graphs or tables should be able to be written in the form abegin mathsize 12px style left parenthesis b right parenthesis to the power of x end style + k. 

    For exponential relationships, tables or graphs must contain at least one pair of consecutive values.

  • Calculator :

    Neutral

  • Clarification :
    Students will compare a linear function and an exponential function
    given in real-world context by interpreting the functions’ graphs.

    Students will compare a linear function and an exponential function
    given in a real-world context through tables.

    Students will compare a quadratic function and an exponential
    function given in real-world context by interpreting the functions’
    graphs.

    Students will compare a quadratic function and an exponential
    function given in a real-world context through tables

  • Stimulus Attributes :
    Items should give a graph or a table.

    Items should be given in a real-world context.

    Items must use function notation

  • Response Attributes :
    Items may require the student to apply the basic modeling cycle.

    Items may require the student to choose an appropriate level of
    accuracy.

    Items may require the student to choose and interpret the scale in a
    graph.

    Items may require the student to choose and interpret units

SAMPLE TEST ITEMS (1)

  • Test Item #: Sample Item 1
  • Question:

    The function f(x) models the value of goods that are imported into the United States, where x is the number of years since 1990. The function g(x) models the value of goods that are exported from the United States.

    If f(x) and g(x) continue to model the importing and exporting of goods, then sometime in 2041, which is 51 years after 1990, f(x)=g(x).

    Determine which function is exponential. Use the table of values to justify your answer.

    Type your answer in the space provided. Be sure to include your function choice.

  • Difficulty: N/A
  • Type: OR: Open Response