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

Name Date

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.

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Copyright

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