Question

G(x) = (2x)³- 4, would be describing which of the following transformations

A. A vertical stretch, scale factor 1/2 and a translation 4 units down.
B. A horizontal compression of scale factor 1/2 and a translation 4 units up.
C. A horizontal compression, scale factor 1/2 and a translation 4 units down.
D. A vertical compression, scale factor 1/2 and a translation 4 units up.

Answer 1

The given function is g(x) = (2x)³ - 4. It represents a vertical stretch, scale factor 1/2, and a translation 4 units down.

Step-by-step explanation:

The given function is g(x) = (2x)³ - 4. To determine the transformations, we can break down the function into two parts: the inside function and the outside function. The inside function, 2x, represents a horizontal compression with a scale factor of 1/2 (since the original x-value is divided by 2). The outside function, ( )³ - 4, represents a vertical translation 4 units down (since 4 is subtracted from the original function). Therefore, the correct answer is A. A vertical stretch, scale factor 1/2, and a translation 4 units down.