The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

(Marvins-Underground-K-12) #1

Teaching Notes 8.11: Evaluating the Greatest Integer Function


The greatest integer function is a special type of piecewise-defined function. Students often have
trouble grasping the meaning of a piecewise-defined function and visualizing the graph. Once
they master the concept, they must apply the definition of the greatest integer function to find
the value of the function.


  1. Explain that a piecewise-defined function is defined by two or more equations over a specific
    domain. Present an example by using the cost of mailing a letter. Letxrepresent the weight
    of the letter in ounces andyrepresent the cost. Therefore:

    • If 0<x≤1,y=$0.44.

    • If 1<x≤2,y=$0.61.

    • If 2<x ≤3,y=$0.73, and so on.



  2. Sketch the graph for your students. Note the meaning of the inequality symbol and how the
    symbols are represented on the graph. An open circle represents the<symbol. A closed
    circle represents the≤symbol.

  3. Review the information and graph on the worksheet with your students. Point out that
    the smaller number is always to the left of a larger number on a number line. Review the
    examples and encourage your students to refer to the graph or a number line to evaluate
    the function. This will help them to identify the ‘‘piece’’ of the graph and use this to find the
    value ofy.


EXTRA HELP:
Remember that integers are the set of counting numbers, their opposites, and zero.

ANSWER KEY:


(1) 0 (2) 5 (3)− 4 (4)− 1 (5) 0 (6)− 5
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(Challenge)Terri is incorrect. She must rewrite the inequality as 4≤x<5.
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