​ Which graph represents the function on the interval [−3, 3] ?

This is the ceiling function shifted down 3 units

To find out which graph is correct....

Let  x  =2

ceiling (2)  - 3=   2  - 3  =  -1

Let x = 2.5

ceiling (2.5) - 3  = 3 - 3  = 0

Let x  = 3

ceiling (3) - 3   =  3 - 3  = 0

The botom right graph is the correct one....

 In mathematics, the functions of the whole part are functions that take a real number and return a whole number, either by excess or by default.
 Function floor (or ground), that to each real number assigns the nearest whole number by defect, that is to say, the greater whole number equal or smaller than that real number.
 Let's evaluate the extremes of the interval
 x = -3
 g (-3) = floor (-3) -2 = -5
 x = 3
 g (3) = floor (3) -2 = 1
 Therefore, the graph that best corresponds to the function in the given interval is the attached graph.

top right graph