How does the graph of g (x) = [x] + 0.5 differ from the graph of f (x) = [x]

When you add a constant value to a function the graph of the function is shifted vertically the number of units indicated by the constant.

In this case, the function g (x) is formed by adding 0.5 to the function f (x) so the graph of g (x) is equal to the graph of f (x) shifted 0.5 units upward.