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?(1 point)
Responses

1/3; compression

3; stretch

3; compression

1/3; stretch

Answer 1

To identify the value of \( k \) based on the ordered pairs (2, 9) and (6, 9), we analyze the transformation:

1. The original ordered pair is (2, 9), which means when \( x = 2 \), \( f(x) = 9 \).
2. The transformed ordered pair is (6, 9), indicating that when \( x = 6 \), the function value is still \( 9 \).

To determine the value of \( k \) and whether the transformation is a stretch or compression, we note the change in the \( x \)-values:

- The original \( x \)-value is \( 2 \).
- The transformed \( x \)-value is \( 6 \).

The relationship can be represented as:

\[
k \cdot x = 6
\]

To find \( k \), we can divide the transformed \( x \)-value by the original \( x \)-value:

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

Now, we need to determine if this represents a stretch or a compression:

- When \( k > 1 \) (which is the case here since \( k = 3 \)), this indicates a stretch.
- When \( k < 1 \), it indicates a compression.

Thus, since \( k = 3 \), it means the transformation results in a stretch.

The correct response is:

**3; stretch**