Greatest Integer Function
If x is a real number, we define [x] as follows:
[x] = n where n is the greatest integer less than or equal to x
Note that n is the first integer to the left of (or equal to) x. For instance,
[0.5] = 0 [1.8] = 1
[Ï€ ] = 3 [e] = 2 [-2.7] = -3
[- 3.4] = -4 [- 0.75] = -1 [-9.3] = -10
The greatest integer function f is defined by f(x) = [x] âˆ€ x âˆˆ R.
The domain of f is R and its range is Z, the set of integers. To draw the graph of
f(x) = [x] we list the x and y coordinates of some points on the graph in the following table.
Values of x |
f(x) = [x] |
. |
. |
-2 â‰¤ x < - 1 |
-2 |
-1 â‰¤ x < 0 |
-1 |
0 â‰¤ x < 1 |
0 |
1 â‰¤ x < 2 |
1 |
2 â‰¤ x < 3 |
2 |
. |
. |