The following ordered pairs came from a function transformation. The original ordered pair is (8,21)

(
8
,
21
)
, and the transformation ordered pair is (2,21)
(
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

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

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

4; stretch
4; stretch

4; compression

1 answer

To determine the value of \( k \) and whether the transformation is a compression or a stretch, we note that the original pair is \( (8, 21) \) and it has been transformed to \( (2, 21) \).

In this case, the \( y \)-value remains the same (21), while the \( x \)-value changes from 8 to 2. To understand the transformation in terms of scaling, we can look at the \( x \)-values:

  1. The \( x \)-value changes from 8 to 2.
  2. This means we are transforming the \( x \)-coordinate, and we find the ratio: \[ k = \frac{2}{8} = \frac{1}{4} \]

Since the \( x \)-coordinate is being multiplied by a factor less than 1 (\(\frac{1}{4}\)), this indicates a stretch in the \( x \)-direction (the input values are effectively spread out).

Thus, the correct identification of \( k \) and the description of the transformation is: \[ \frac{1}{4}; \text{ stretch} \]

The correct response from the options you provided is: Start Fraction 1 over 4 End Fraction ; stretch.