Question

Which of the following best describes the transformation from the solid-line graph to the dotted-line graph and correctly states the factor k? the parent has x points at -1 and 1, and the altered one has x points at -2 and 2 (1 point) Responses horizontal compression with a factor k = 2 horizontal compression with a factor k = 2 horizontal compression with a factor k = 0.5 horizontal compression with a factor k = 0.5 horizontal stretch with a factor k = 0.5 horizontal stretch with a factor k = 0.5 horizontal stretch with a factor k = 2 horizontal stretch with a factor k = 2

Answer 1

To analyze the transformation from the solid-line graph to the dotted-line graph based on the x-intercepts provided:

The parent graph has x-intercepts at -1 and 1. The altered graph has x-intercepts at -2 and 2.

This transformation changes the x-values such that each x-value in the original graph is scaled by a factor that causes the x-intercepts to become twice as far from the origin. Since -1 and 1 became -2 and 2, we can determine that the transformation involves a horizontal compression by a factor.

The rule for horizontal transformations is:
- If the x-values in the transformed function are larger (farther from the origin), then it's a horizontal compression.
- If the x-values in the transformed function are closer (less far from the origin), then it's a horizontal stretch.

In this case, the new x-intercepts are double those of the original, meaning we are compressing the x-axis by a factor of 0.5.

Therefore, the correct answer is: **horizontal compression with a factor k = 0.5**.