Name Date
WORKSHEET 8.11: EVALUATING THE GREATEST INTEGER
FUNCTION
-------------------------------------------------------------------------------------
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|]=
- Visualizeordrawanumberline.
- Find the value ofxon the number line and determine which two integersxis between.
- 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]].
- f(0) 2. f(5.2)
- f(− 3 .5) 4. f(−1)
- 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
Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.