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MAFS.912.A-REI.4.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Algebra: Reasoning with Equations & Inequalities
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Represent and solve equations and inequalities graphically. (Algebra 1 - Major Cluster) (Algebra 2 - Major 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: EE item(s)
  • Also assesses: 
    MAFS.912.A-REI.4.10

  • Assessment Limits :
    In items where a function is represented by an equation, the function
    may be an exponential function with no more than one translation, a
    linear function, or a quadratic function.

    In items where a function is represented by a graph or table, the
    function may be any continuous function. 



     

  • Calculator :

    Neutral

  • Clarification :
    Students will find a solution or an approximate solution for f(x) = g(x)
    using a graph.

    Students will find a solution or an approximate solution for f(x) = g(x)
    using a table of values.

    Students will find a solution or an approximate solution for f(x) = g(x)
    using successive approximations that give the solution to a given
    place value.

    Students will justify why the intersection of two functions is a solution
    to f(x) = g(x).

    Students will verify if a set of ordered pairs is a solution of a function.

  • Stimulus Attributes :
    Items may be set in a mathematical or real-world context.

    Items may use function notation.

    Items must designate the place value accuracy necessary for
    approximate solutions.

  • Response Attributes :
    Items may require the student to complete a missing step in an
    algebraic justification of the solution of f(x) = g(x).

    Items may require the student to explain the role of the x-coordinate
    and the y-coordinate in the intersection of f(x) = g(x).

    Items may require the student to explain a process.

    Items may require the student to record successive approximations
    used to find the solution of f(x) = g(x).

SAMPLE TEST ITEMS (1)

  • Test Item #: Sample Item 1
  • Question:

    Cora is using successive approximations to estimate a positive solution to f(x)=g(x), where 

    f(x)=x²+13 and g(x)=3x+14. The table shows her results for different input values of x.

    Use Cora's process to find the positive solution, to the nearest tenth, of f(x)=g(x).

  • Difficulty: N/A
  • Type: EE: Equation Editor