The notation for [[ … ]] is used for the Greatest Integer Function. The graph of this function is called a stepladder, simply because it resembles one. It’s not that hard to graph although it’s quite different from the usual graphs we know. It would help a lot if you can see a sample graph of any Greatest Integer Function.

If you can’t find one, try plotting values for x and obtain the corresponding values for y (or g(x)) to give you a better idea how the graph looks like. For example, if x = 1, y = 2; if x=1.2, y = 2, if x=1.4, y =2, if x=1.5, y=3, if x=1.9, y=3, if x=2, y=4, if x=2.499999, y=4, if x=2.5, y=5, and so on. It’s might be a little more for negative values though. If x= -1, y= -2, if x= -1.1, y= -3, if x= -1.5, y=-3, if x= -1.6, y= -4, if x= -1.99, y = -4, if x= -2, y= -4, if x= -2.00001, y= -5, and so on.

If you graph this correctly, it should look like a stepladder with the leftmost part of each step a dot and the rightmost part a circle (or a small hollow dot).

The domain of g(x) is all real numbers (meaning any real value for x is permissible), and its range is all integers (because y is always an integer).

It’s actually fun to try and discover how the graph of this function looks like, so please try it!

Hope this helps.