Standard #: MAFS.912.F-IF.3.8 (Archived Standard)


This document was generated on CPALMS - www.cpalms.org



Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  1. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
  2. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = , y = , y = , y = , and classify them as representing exponential growth or decay.


General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Functions: Interpreting Functions
Cluster: Analyze functions using different representations. (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 - Archived
Assessed: Yes

Test Item Specifications

    Also assesses:

    MAFS.912.A-APR.2.3

    MAFS.912.F-IF.3.7

    Assessment Limits :
    For F-IF.3.7, items are limited to linear, quadratic, and exponential
    functions.

    For A-APR.2.3, the leading coefficient should be an integer and the
    polynomial’s degree is restricted to 3 or 4. The polynomial function
    should not have a zero with multiplicity. The polynomial should be
    given in factored form.

    For F-IF.3.8a, items that require the student to transform a quadratic
    equation to vertex form, b/a must be an even integer.

    For F-IF.3.7e and F-IF.3.8b, exponential functions are limited to simple
    exponential growth and decay functions and to exponential functions
    with one translation. Base e should not be used.

    For F-IF.3.8, items may specify a required form using an equation or using common terminology such as standard form. In items that require the student to interpret the vertex or a zero of a quadratic function within a real-world context, the student should interpret both the x-value and the y-value. 

    For F-IF.3.7a, quadratic functions that are given in the form y = ax² + bx + c, a, b, and c must be integers. Quadratic functions given in vertex form y = a(x – h)² + k, a, h, and k must be integers. Quadratic functions given in other forms should be able to be rewritten and adhere to one of the two previous forms.

     

    Calculator :

    Neutral

    Clarification :
    Students will identify zeros, extreme values, and symmetry of a
    quadratic function written symbolically.

    Students will classify the exponential function as exponential growth
    or decay by examining the base, and students will give the rate of
    growth or decay.

    Students will use the properties of exponents to interpret exponential
    expressions in a real-world context.

    Students will write an exponential function defined by an expression
    in different but equivalent forms to reveal and explain different
    properties of the function, and students will determine which form of
    the function is the most appropriate for interpretation for a realworld context.

    Students will find the zeros of a polynomial function when the
    polynomial is in factored form.

    Students will create a rough graph of a polynomial function in
    factored form by examining the zeros of the function.

    Students will use the x-intercepts of a polynomial function and end
    behavior to graph the function.

    Students will identify the x- and y-intercepts and the slope of the
    graph of a linear function.

    Students will identify zeros, extreme values, and symmetry of the
    graph of a quadratic function.

    Students will identify intercepts and end behavior for an exponential
    function.

    Students will graph a linear function using key features.

    Students will graph a quadratic function using key features.

    Students will graph an exponential function using key features.

    Students will identify and interpret key features of a graph within the
    real-world context that the function represents.

    Stimulus Attributes :
    Items may require the student to identify a correct graph.

    Items may be set in a mathematical or real-world context.

    For F-IF.3.8, items must use function notation.

    For F-IF.3.7, items may use an equation or a function.

    Items should not require the student to complete a sign chart for a
    polynomial. 

    Response Attributes :
    For F-IF.3.7, 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.

    Items may require the student to provide the answer in a specific
    form.

    Responses with square roots should require the student to rewrite
    the square root so that the radicand has no square factors.



Sample Test Items (2)

Test Item # Question Difficulty Type
Sample Item 1

A bird drops a stick from the top of Miami Tower. The height of the stick after x seconds is given by 

f(x)=625-16x²

Select all the correct interpretations of the coordinates of the point at the maximum of the function f(x).

N/A MS: Multiselect
Sample Item 2

A bird drops a stick from the top of Miami Tower. The height of the stick after x seconds is given by 

f(x)= 625-16x².

What is the maximum value of f(x)?

N/A EE: Equation Editor


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