Graphing Greatest Integer Function

How do I graph f(x) = [[ x ]] by hand?

I know the graph looks like steps but I don't get it.

Explain in steps.

What about if the greatest integer function is added to a number or subtracted by a number?

Sample A

Graph f(x) = [[ x ]] + 1.

Sample B

Graph f(x) = [[ x ]] - 1.

 

The Greatest Integer Function is denoted by y = [x].

For all real numbers, x, the greatest integer function returns the largest integer
less than or equal to x. In essence, it rounds down a real number to the nearest integer.

For example: [1] = 1 [1.5] = 1 [3.7] = 3 [4.3] = 4
Beware! [-2] = -2 [-1.6] = -2 [-2.1] = -3 [-5.5] = -6
see attached graph

here is another example, nicely explained:

 

I forgot to search You Tube. Thanks for the video clip.