Question

The following ordered pairs came from a function transformation. The original ordered pair is (8,21)
, and the transformation ordered pair is (2,21)
. Which of the following correctly identifies the value of k and describes whether it is a compression or a stretch?(1 point)
Responses

1/4
; compression
Start Fraction 1 over 4 End Fraction ; compression

4; compression
4; compression

1/4
; stretch
Start Fraction 1 over 4 End Fraction ; stretch

4; stretch

Answer 1

To identify the value of \( k \) and whether the transformation is a compression or a stretch, we can analyze how the \( x \)-coordinate of the ordered pair changes from the original to the transformed pair.

The original pair is \( (8, 21) \) and the transformed pair is \( (2, 21) \).

The \( y \)-coordinate remains the same, which indicates no vertical transformation has occurred. We only need to focus on the \( x \)-coordinates to determine the horizontal transformation.

The transformation can be expressed as:

\[
x' = k \cdot x
\]

Where:
- \( x' = 2 \) (the transformed \( x \)-coordinate)
- \( x = 8 \) (the original \( x \)-coordinate)

Plugging in the values gives us:

\[
2 = k \cdot 8
\]

Now, solving for \( k \):

\[
k = \frac{2}{8} = \frac{1}{4}
\]

Now we determine if this is a compression or a stretch:
- A \( k \) value less than 1 indicates a compression.
- A \( k \) value greater than 1 indicates a stretch.

Since \( k = \frac{1}{4} \), it indicates a compression.

The correct response is:

**1/4; compression**