Question

What does the transformation f(x)↦9f(x) do to the graph of f(x)?

Answer 1

The transformation \( f(x) \mapsto 9f(x) \) affects the graph of the function \( f(x) \) by vertically stretching it by a factor of 9. This means that for every point on the graph of \( f(x) \), the y-coordinates will be multiplied by 9.

Here's how it works:

- If the original function \( f(x) \) has a point \( (x, y) \) on its graph, where \( y = f(x) \), then after the transformation, this point will move to \( (x, 9y) \), or specifically \( (x, 9f(x)) \).
- For positive values of \( f(x) \), the transformed graph will rise higher above the x-axis by a factor of 9.
- For negative values of \( f(x) \), the transformed graph will extend further below the x-axis by the same factor.

In summary, the transformation scales the graph vertically, making it taller (or deeper if it’s below the x-axis). It does not change the x-coordinates or the shape of the graph, just how far the points extend up or down.