Question

If f(x) = x and g(x) = -2x, how has f(x) been transformed to get g(x)?

Answer 1

The transformation in f(x) includes a reflection about the x-axis and a vertical stretch (or compression) by a factor of 2.

Step-by-step explanation:

The function g(x) = -2x is a transformation of the function f(x) = x.

In this case, the transformation is a reflection about the x-axis and a vertical stretch (or compression) by a factor of 2.

Here's how:

1. A reflection about the x-axis means that the positive y-values of f(x) become negative in g(x).
2. A vertical stretch (or compression) by a factor of 2 means that the vertical distance between points on the graph is doubled (or halved).

So, f(x) = x transformed to g(x) = -2x results in a graph that is reflected about the x-axis and vertically stretched (or compressed) by a factor of 2.