Question

The following ordered pairs came from a function transformation. The original ordered pair is (8,21), and the transformation ordered pair is (2,21). Which of the following correctly identifies the value of k and describes whether it is a compression or a stretch?(1 point)
Responses

4; compression

1/4; stretch

4; stretch

1/4; compression

Answer 1

To determine the value of \( k \) and whether it represents a compression or a stretch, we can analyze how the x-coordinates of the ordered pairs changed.

The original ordered pair is (8, 21), and the transformed ordered pair is (2, 21). The transformation affects only the x-coordinate:

1. The original x-coordinate is 8.
2. The transformed x-coordinate is 2.

To find \( k \):

\[
k = \frac{\text{original x}}{\text{transformed x}} = \frac{8}{2} = 4
\]

Since the x-coordinate decreased from 8 to 2, this indicates a **compression** in the horizontal direction.

Thus, the correct response is:

**4; compression**