Common Core 2
Guided Notes
Name _______________________
Greatest Interger Function
The Greatest Integer Function The Step Function or the Floor Function
f (x) = [x]
This function takes the input and finds the greatest integer to that
number without going over. Think the Price is Right!
Examples:
Answers
Examples:
Answers:
1. [7.35] =
7
3. [-2.5]
-3
4
2.   =
3
1
 10 
4.  
 5
-2
Graphing the Greatest Integer Function
The greatest integer function got its nickname, the step function, from its graph.
f (x) = [x]
We have to use closed circles and
open circles on the end of the
“steps” to make sure that the graph
stays a function. If we had no open
circles, then the steps would
overlap one another at the ends,
and would not pass the vertical line
test (therefore, not being a
function). Make sure you mark your
open and closed circles properly.
x
-2.00
-1.75
-1.5
-1.25
-1.00
-0.75
-0.5
-0.25
0.00
0.25
0.5
0.75
1.00
1.25
1.5
f (x)
-2
-2
-2
-2
-1
-1
-1
-1
0
0
0
0
1
1
1
You have to make a T-chart
to figure out where your
steps go. Here, we can see
that the steps are –2
between –2 and –1, -1
between –1 and 0, etc.
Transformations of the Greatest Integer Function
Don’t forget the transformations do not change!
Graphing Form: y = 𝑎⟦𝑏(𝑥 − ℎ)⟧ + 𝑘
So (h, k) is a starting point for your steps.
The length of your steps is 1/b.
The space between your steps (vertically) is a.
If a is positive the steps go up to the right and is a is negative then the steps go down to the right.
Example: Graph 𝑓(𝑥) = 2⟦𝑥 − 3⟧ + 1
Start (3, 1)
Step length 1
Step height 2
Example 2: Graph 𝑦 = ⟦2𝑥 + 4⟧ − 5
Get in graphing form! 𝑦 = ⟦2(𝑥 + 2)⟧ − 5
Start (-2, -5)
Step length ½
Step height 1