Question

For the function (x)=|x|-3, what transformation does "vertical shrink by a factor of 1/3" represent?

a) Reflection across the x-axis
b) Vertical stretch by a factor of 3
c) Horizontal compression by a factor of 3
d) Vertical compression by a factor of 1/3

Answer 1

A 'vertical shrink by a factor of 1/3' means that the graph of the function is subjected to a vertical compression by a factor of 1/3, which is option (d) in the provided choices.

Step-by-step explanation:

The transformation "vertical shrink by a factor of 1/3" for the function f(x)=|x|-3 means that the graph of the function is scaled down vertically by a factor of 1/3 of its original size. This type of transformation is known as a vertical compression. It does not reflect the graph across the x-axis, nor does it stretch it vertically or compress it horizontally. Instead, all the points on the graph of the function move closer to the x-axis by a factor of 1/3, making the graph appear 'flatter' but still maintaining the general shape of the original function.

Given the options provided, the transformation that corresponds to a vertical shrink by a factor of 1/3 is described by option (d) Vertical compression by a factor of 1/3.