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

For compression
For stretch

Answer 1

To determine the value of \( k \) and whether the transformation is a compression or a stretch, we can look at the transformation of the x-coordinates in the ordered pairs.

- The original ordered pair is \( (8, 21) \)
- The transformed ordered pair is \( (2, 21) \)

To identify the value of \( k \) in terms of a horizontal transformation, we can compare the x-coordinates:

The transformation from 8 to 2 can be described by the equation:
\[
x' = k \cdot x
\]
Plugging in the values:
\[
2 = k \cdot 8
\]

Solving for \( k \):
\[
k = \frac{2}{8} = \frac{1}{4}
\]

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

Thus, the correct identification is:
- The value of \( k \) is \( \frac{1}{4} \).
- This represents a horizontal compression.

So to answer:
- \( k = \frac{1}{4} \)
- It is a **compression**.