Question

The following ordered pairs came from a function transformation. The original ordered pair is (2,9)
(
2
,
9
)
, and the transformation ordered pair is (6,9)
(
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; stretch
3; stretch

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

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

3; compression

Answer 1

To determine the value of \( k \) and whether it represents a compression or a stretch in the context of a function transformation, we can analyze the changes in the \( x \)-coordinate of the ordered pairs.

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

### Step 1: Identify the transformation in the \( x \)-direction

To find the value of \( k \):
- The original \( x \) value is \( 2 \).
- The transformed \( x \) value is \( 6 \).

To find the value of \( k \), we can use the formula for horizontal scaling, which is given by:

\[
k = \frac{x_{\text{transformed}}}{x_{\text{original}}}
\]

Substituting in the values:

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

### Step 2: Determine whether it is a compression or a stretch

In this context:
- If \( k > 1 \), it indicates a **stretch**.
- If \( k < 1 \), it indicates a **compression**.

Since \( k = 3 \), which is greater than 1, this indicates a stretch.

### Conclusion

The value of \( k \) is \( 3 \), and it is a **stretch**.

So the correct answer is:
**3; stretch**.