Question

F(x)=-2x reflection across the x-axis, and a vertical compression by a factor of 1/8

Answer 1

To reflect the function f(x) = -2x across the x-axis and compress it vertically by 1/8, the transformed function is g(x) = 1/4x. This involves negating the function and then multiplying by 1/8.

Step-by-step explanation:

To transform the function f(x) = -2x by reflecting it across the x-axis and applying a vertical compression by a factor of 1/8, we follow two steps:

1. Reflection across the x-axis is achieved by multiplying the function by -1, which changes the sign of the output.
2. Vertical compression by a factor of 1/8 means we multiply the entire function by 1/8.

Therefore, the transformed function becomes: g(x) = -1/8(-2x) = 1/4x.

This new function, g(x), is the result of the specified transformation of the original function f(x).