graph function over interval

This is known as a "ceiling" function  shifted down 3 units

The ceiling function basically "rounds up" a value UNLESS that value is already an nteger

Look at the first graph at the top left

The point (1.5, 3)  is on this graph

But Celiing (1.5)  = 2

So

Ceiling (1.5) - 3    =  2 - 3   =  -1

So  this graph is not correct

Look at the graph at the top right

The point (2, 0) is on the graph

Ceiling 2   = 2

But

Ceiling 2 - 3  =   -1

So....this graph is not correct

Look at the graph at the bottom left

This graph is not correct....the point (0, 2) is on the graph

Ceiling (0) = 0

But

Ceiling (0) - 3  =   -3

So  .....this graph is incorrect

Look at the graph at the bottom right

The point (2, - 1)  is on the graph

Ceiling (2) = 2

So

Ceiling (2) - 3   =   2 - 3   = -1

Also....when x = 3.....y = 0   which is correct

So.....you were correct.....this is the correct graph.....!!!!!