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

4; compression
4; compression

4; stretch
4; stretch

14
; stretch
Start Fraction 1 over 4 End Fraction ; stretch

14
; compression
Start Fraction 1 over 4 End Fraction ; compression

Answer 1

To determine the value of \( k \) and whether the transformation is a compression or a stretch, we can analyze the original ordered pair \((8, 21)\) and the transformed ordered pair \((2, 21)\).

1. **Identify the change in the x-values**:
- Original x-value: \( 8 \)
- Transformed x-value: \( 2 \)

The change in the x-values can be expressed in terms of \( k \) as \( k \cdot 8 = 2 \).

To find \( k \), we rearrange this equation:
\[
k = \frac{2}{8} = \frac{1}{4}
\]

2. **Determine if it's a compression or a stretch**:
- A value of \( k < 1 \) implies a **compression** (the x-values are made smaller).
- A value of \( k > 1 \) implies a **stretch** (the x-values are made larger).

Since \( k = \frac{1}{4} \), and it is less than 1, this indicates a **compression**.

In conclusion, the correct response is:

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