Question

How does the graph of g(x)=⌈x⌉+0.5 differ from the graph of f(x)=⌈x⌉?

Answer 1

In general, a positive constant moves a function upwards and a negative value moves it downwards. Thus, g(x)=⌈x⌉+0.5 is 0.5 units above f(x)=⌈x⌉, as shown in attached picture.

To shift a function left, you add units to the independent variable.To shift it right, you subtract a constant from "x".
Example:
h(x)=⌈x+1⌉ is 1 unit left to f(x).