Final answer:
Replacing a function f(x) with f(x - 4) results in a horizontal shift of the original graph 4 units to the right along the x-axis.
Step-by-step explanation:
When analyzing the transformation of a function f(x), it is essential to understand the effects of replacing it with f(x – 4). This specific transformation is known as a horizontal translation.
As stated in algebra, when we have a function f(x) and replace it with f(x – d), the graph of the function shifts to the right by a distance of 'd' units. In the context of our question, replacing f(x) with f(x – 4) moves the original graph of the function 4 units to the right on the x-axis.
This means that for any value of 'x', the value of the newly transformed function at 'x' is the same as the value of the original function at 'x - 4'.
If the function represents a wave, the crest, troughs, and all other points on the wave would be displaced 4 units to the right.