Question

Define a greatest integer function. Draw its graph and find its domain and range.

Answer 1

The function f : R → R define by f(x) = [x], x ∈ R assumes the value of the greatest integer, less than or equal to x. Such a’ function is called the greatest integer function or step function. We have

[x] = -2 for – 2 ≤ x < -1

[x] = -1 for -1 ≤ x < 0 

[x] = 0 for 0 ≤ x ≤ 1 

[x] = 1 for 1 ≤ x < 2 

[x] = 2 for 2 ≤ x < 3. 

Hence, domain of f = R and range = Z.