The following ordered pairs came from a function transformation. The original ordered pair is (2,9)

Question

, and the transformation ordered pair is (6,9)
. Which of the following correctly identifies the value of k and describes whether it is a compression or a stretch?(1 point)
Responses

3; compression
3; compression

3; stretch
3; stretch

1/3
; compression
Start Fraction 1 over 3 End Fraction ; compression

1/3
; stretch
Start Fraction 1 over 3 End Fraction ; stretch

Answer 1

To determine the value of \( k \) and whether the transformation is a compression or a stretch, we need to analyze how the transformation affects the x-coordinate of the original ordered pair (2, 9) to the transformed ordered pair (6, 9).

1. The original x-coordinate is 2, and the transformed x-coordinate is 6.

2. To find \( k \), we can use the formula for transformations in function behavior which relates the original x-coordinate and the transformed x-coordinate as follows:

   \[ k \cdot x = \text{transformed x} \]

   Substituting the values:

   \[ k \cdot 2 = 6 \]

   To find \( k \), we solve for \( k \):

   \[ k = \frac{6}{2} = 3 \]

3. Since \( k = 3 \) is greater than 1, this indicates that the transformation stretches the function.

Thus, the correct answer is:

3; stretch