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.