Greatest Integer Function
You don’t want to buy half of a CD or a third of a car. Sometimes, fractional
amounts just won’t do. In those situations, you can use a function called the
Greatest Integer Function. When you see   bracketing a variable, it is read the
greatest integer of.
The greatest integer function is the function, f, such that f ( x)  x  where x  is
the greatest integer less than or equal to a real number, x.
For example, when x = 2.7, x  = 2. When x = -2.7, x  = -3.
x
f ( x)  x 
-4 < x < -3
-3 < x <-2
-2 < x < -1
-1 < x < 0
0<x<1
1<x<2
2<x<3
3<x<4
-4
-3
-2
-1
0
1
2
3
The graph of the greatest integer function looks like a series of steps. That’s why
it is sometimes called a step function.
p. 124 #21
a. Sketch the graph of y = [x]. Hint: Use the table given in the explanation to help
you graph the function.
b. Give the domain and range of the greatest integer function.