Question

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

3; compression
3; compression

13
; compression
Start Fraction 1 over 3 End Fraction ; compression

13
; stretch

Answer 1

To determine the value of \( k \) and whether the transformation is a compression or a stretch, we first need to understand how the transformation affects the input \( x \) of the function.

The original ordered pair is \( (2, 9) \), and the transformed ordered pair is \( (6, 9) \).

Here, the output \( y \) remains the same (9), while the input \( x \) changes from 2 to 6.

To calculate the scaling factor \( k \):

1. We identify the scaling factor based on the change in \( x \):
\[
k = \frac{\text{new } x}{\text{old } x} = \frac{6}{2} = 3
\]

Since \( k > 1 \), this indicates a **stretch** in the horizontal direction because the \( x \)-values are increasing by a factor of 3.

So, the correct identification is:
- \( k = 3 \); stretch

The final answer is:
**3; stretch**