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.- 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.
- 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. - 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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