Final answer:
Adding or subtracting a constant to the x variable in a function results in a horizontal shift of the graph to the left or right respectively, without altering the shape of the graph.
Step-by-step explanation:
When you add or subtract a constant to the x variable in a function, you are creating what is known as a horizontal shift or translation. Adding a constant to x would shift the graph to the left, while subtracting a constant from x shifts it to the right. For example, if you have the function y = f(x) and you create a new function y = f(x - c), where c is a positive constant, the graph of the new function will be the same as the original, but shifted c units to the right.
Conversely, if you have the function y = f(x + c), this will shift the graph c units to the left. These shifts do not affect the shape of the graph but merely change the position of the graph on the coordinate plane. Understanding this concept is particularly useful in subjects such as economics, where functions are often used to model and predict cause and effect.