I think Alex is complicating this a bit much.
As far as I'm aware, you fully understand functions, just not how to graph them.
Well, it's pretty easy once you know that:
x = your input.
y = your output.
so say your x = 4. Then on the X Line, you are +4 across.
Function: x + 1
So the x value is 4 and the y value is 5. You can now graph your line. As Alex said, there will be much more complex types of functions where x will be squared and this will give you a parabola.