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
4; compression

4; stretch
4; stretch

1/4
; stretch
Start Fraction 1 over 4 End Fraction ; stretch

1/4
; compression
Start Fraction 1 over 4 End Fraction ; compression

Answer 1

To analyze the transformation from the original ordered pair (8, 21) to the transformed ordered pair (2, 21), we can consider the changes in the x-coordinates.

The original x-coordinate is 8, and after the transformation, the new x-coordinate is 2.

To determine the value of k, we can use the formula for horizontal transformations, which states that if you have a transformation of the form \( (x, y) \) to \( (kx, y) \), then:

\[
k = \frac{\text{new x}}{\text{original x}} = \frac{2}{8} = \frac{1}{4}.
\]

Since \( k = \frac{1}{4} \), this indicates a horizontal compression because the value of k is less than 1. A horizontal compression means that every x-coordinate is being squeezed closer to the y-axis.

Therefore, the correct choice is:

**1/4; compression**.