Question

What does the transformation f(x)↦f(x)–3 do to the graph of f(x)?

Answer 1

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.