Final answer:
The function f(x) = x modified to f(x) = x - 3 shifts the graph of the function horizontally to the right by 3 units and decreases the y-intercept, causing a downward shift while maintaining parallelism to the original line.
Step-by-step explanation:
When the base linear function f(x) = x is modified to become f(x) = x - 3, this represents a horizontal shift of the graph of the function to the right by 3 units. This happens because each output value of f(x) is decreased by 3 compared to the input value. In terms of the y-intercept of the line, the new function has a smaller intercept, meaning it would graphically shift down from the old origin, but remain parallel to the original line. This adjustment is useful when solving models with algebra, as economists and scientists do when answering specific questions such as predicting the unemployment rate based on economic growth or understanding demand curves in business.