Final answer:
The function after a vertical compression by a scale factor of 1/8 is f(x) = 1/8 * |x|. This compresses the original V shape of the absolute value function closer to the x-axis.
Step-by-step explanation:
The question at hand involves transforming a given function by applying a vertical compression. Initially, we have the function f(x) = |x|, which is an absolute value function that forms a "V" shape when graphed, reflecting at the origin (0,0). A vertical compression by a scale factor of 1/8 means that we multiply the output of the function by 1/8. Therefore, the new function after the vertical compression will be f(x) = 1/8 * |x|. This new function will still have the same shape as the original absolute value function, but it will be "flattened" towards the x-axis, making the V shape less steep. An understanding of how transformations alter the graph of a function is a key concept in algebra and pre-calculus.
The function after a vertical compression by a scale factor of 1/8 is f(x) = 1/8 * |x|. This compresses the original V shape of the absolute value function closer to the x-axis.