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
Start Fraction 1 over 3 End Fraction ; compression

3; stretch
3; stretch

3; compression
3; compression

1/3
; stretch

Answer 1

To determine the value of \( k \) in the context of the transformation from the ordered pair (2, 9) to (6, 9), we need to see how the \( x \)-coordinate changes.

The original \( x \)-coordinate is 2, and after the transformation, it becomes 6. You can express this transformation using \( k \) such that:

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

Substituting in the values we have:

\[
k \cdot 2 = 6
\]

Solving for \( k \):

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

Now let's determine whether this represents a stretch or a compression.

When \( k > 1 \), the transformation results in a stretch. When \( 0 < k < 1 \), it results in a compression. Since \( k = 3 \) and it is greater than 1, this indicates a stretch.

Thus, the correct identification is:

**3; stretch**.