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

(Marvins-Underground-K-12) #1
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WORKSHEET 8.11: EVALUATING THE GREATEST INTEGER
FUNCTION
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The greatest integer function is defined as the greatest (largest) integer that is less than or
equal tox. It is denoted asf(x)=[[x]]. Its graph is shown below. Follow the steps below the
graph to evaluate the greatest integer function.

x

y

− 2 − 112

2

1

− 1

− 2

2 if 2 ≤x< 3

1 if 1 ≤x< 2

0 if 0 ≤x< 1

−1 if − 1 ≤x< 0

−2 if − 2 ≤x<− 1

[|x|]=


  1. Visualizeordrawanumberline.

  2. Find the value ofxon the number line and determine which two integersxis between.

  3. Use the number line to find the largest integer that is less than or equal tox.


EXAMPLES
f(x)=[[x]].Findf(1.5),f(−1.5), andf(2).
f(1.5)=1. 1.5 is between 1 and 2. 1 is the largest integer that is less than 2.
f(−1.5)=−2.−1.5 is between−1and−2.−2 is the largest integer that is less than−1.5.
f(2)=2 because 2 is equal to 2.

DIRECTIONS: Find the values iff(x)=[[x]].



  1. f(0) 2. f(5.2)

  2. f(− 3 .5) 4. f(−1)

  3. f(0.25) 6. f(− 4 .1)


CHALLENGE:Terri tried to summarize all of the values ofxso that [[x]]=4.
She said that 4 < x≤5. Is she correct? Explain your answer.

295

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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