Main Menu Units by Performance Expectation Units by Strand Units by Topic About the Capstone Course

Understanding and Applying Functions

Students will be able to recognize, use, and interpret various functions and their representations, including verbal descriptions,
tables, equations, and graphs to make predictions and analyze relationships in solving complex, real-world mathematical problems.

  1. The student will transfer between and analyze multiple representations of functions, including algebraic formulas, graphs, tables, and
    words. Students 
    will select and use appropriate representations for analysis, interpretation, and prediction.

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  2. The student will investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.

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  3. The student will recognize the general shape of function (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions.

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  4. The student will use knowledge of transformations to write an equation, given the graph of a function
    (linear, quadratic, exponential, and logarithmic). Δ

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  5. The student will investigate and analyze functions (linear, quadratic, exponential, and logarithmic families) algebraically and graphically.
    Key concepts include Δ

    a) continuity;

    b) local and absolute maxima and minima;

    c) domain and range, including limited and discontinuous domains and ranges;

    d) zeros;

    e) x- and y-intercepts;

    f) intervals in which a function is increasing or decreasing;

    g) asymptotes;

    h) end behavior;

    i) inverse of a function; and

    j) composition of multiple functions.

    k) finding the values of a function for elements in its domain; and

    l) making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.

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  6. The student will determine optimal values in problem situations by identifying constraints and using linear programming techniques.