The transformation \( f(x) \mapsto f(x) - 3 \) represents a vertical shift of the graph of the function \( f(x) \). Specifically, this transformation moves the entire graph of \( f(x) \) down by 3 units.
In general, when you subtract a constant from a function, it results in a downward shift. If you were to add a constant instead (e.g., \( f(x) + 3 \)), it would shift the graph upward by that amount.
So, for the transformation \( f(x) - 3 \), every point on the graph of \( f(x) \) will be lowered by 3 units on the vertical axis.
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