Why does adding a constant to a function's input (as in f(x-a)) shift the plot of the function along the x-axis?

Imagine the function f(x) as a black box which takes in any value x and produces an output y. The black box acts on its input according to a rule which produces a unique value of y for a given x. If the black box becomes f(x-a) then whenever we throw a value into it a is subtracted from this value before the usual rule is applied. Thus if we imagine a plot of the function we see that any given point on the x-axis will become associated with the y-value originally paired with an adjacent point on the x-axis separated by a distance a.

For example, if we throw 4 into f(x-2)=(x-2)^2 we get 4. But we also get 4 if we throw 2 into f(x)=x^2. Similarly, we get the same output from inputting 2 into f(x-2) as from inputting 0 into f(x) and so on. Drawing an example like f(x)=x^2 and trying some example inputs and outputs should allow you to visualise how this will shift the plot depending on the value of the constant a.