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

f(x)=[x]−3

Are the brackets around the x a floor or ceiling function? I can't tell, so I am unable to tell what it is.

It's floor.

y = floor ( x) - 3

Let's plot a few values

x = 1 ....floor = 1 so y = -2

x = 1.5 ....floor = 1 so y = -2

x = 2 ....floor = 2 so y = -1

So....the points (1, - 2) (1.5, -2) and ( 2, - 1) are on the graph

Notice that these points only exist on graph "D"