we will select each options and then verify it
option-A:
we know that
greatest integer function is for all real numbers, x, the greatest integer function returns the largest integer. less than or equal to x
Here , we can see that between 0 to 1 ... then value of y=0..which is less than 1
so, this is TRUE
option-B:
f(4.5)=5
since, this is greatest integer function
so, for x=4.5 , y should be 4
so, this is FALSE
option-C:
Since, this does not satisfy horizontal line test
so, it is not one to one
so, this is FALSE
option-D:
we can see that
f(0)=0
when x=0 , y=0
we are given point at origin
so, this is TRUE
option-E:
we can see that
f(1.4)=1
Since, it is greatest integer function
So, when x=1.4 and y=1
so, this is TRUE