Question

The following ordered pairs come from a function transformation the original ordered pair is 8, 21 and the transformation ordered pair is two, 21 which of the following correctly identifies the value of k and describes whether it is a compression or a stretch
1/4 compression

4 compression
4 stretch

Answer 1

To analyze the transformation from the original ordered pair (8, 21) to the transformed ordered pair (2, 21), we focus on the x-value since the y-value (21) remains unchanged.

The original x-value is 8, and the transformed x-value is 2. The transformation can be characterized by determining the factor \( k \) that changes 8 into 2.

To find \( k \), we can use the formula for a horizontal transformation, which involves division of the x-values:

\[
k = \frac{\text{original x}}{\text{transformed x}} = \frac{8}{2} = 4
\]

Now, to identify whether this transformation is a compression or a stretch:

- A horizontal compression by a factor of \( k \) means the distance from the y-axis is reduced; in general, this happens when \( k > 1 \).
- A horizontal stretch by a factor of \( k \) means the distance from the y-axis is increased; this happens when \( k < 1 \).

Since \( k = 4 > 1 \), this indicates a horizontal **compression**.

Therefore, the correct identification is:

**k = 4, and it is a compression.**