Here is one way to understand how the graph of f(x) translates to f(x-1):
Suppose that your input value is x=3. Then the corresponding point on the graph of f is (3, f(3)). If you now use the same input value for f(x-1), the input is again x=3, but now, before you evaluate the function, you subtract 1. The corresponding point is (3, f(3-1)) or (3, f(2)). In other words, at x=3, the new point has the same height (or y value) as f(2). This can be thought of as a translation of the point (3, f(3)) to the right by one unit, or (3, f(2)).
