Write domain and range of greatest integer function

The function f : R → R defined by 

f(x) = [x] for all xR 

is called the greatest  integer function or step function.

The domain of the greatest integer function is the set R of all real numbers and the range is the set Z of all integers as it attains only integer values. 

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DOMAIN ={ all real numbers} ,  since  the co-ordinates of the X-axis  can be +ive , -ive or be  in fractions .

RANGE ={  1 , 0 , -1} ,( because when ever we take  the value  of any real no. say , X to be  0 , we always get the  G.I.F  as 0. Similarly when X<0 , the G.I.F  is  always  -1   and  when  X>0  the  G.I.F  is always  1.)

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