6 Select the statement which correctly completes the sentence
“The effect of a transformation is to …”
A stretch the higher values in the data
B maintain the distance between values
C stretch the lower values in the data
D compress the higher values in the data
E maintain the order of the values in the data

Ask by Daniels Little. in Australia

Mar 27,2025

Question

6 Select the statement which correctly completes the sentence
“The effect of a transformation is to …”
A stretch the higher values in the data
B maintain the distance between values
C stretch the lower values in the data
D compress the higher values in the data
E maintain the order of the values in the data

Ask by Daniels Little. in Australia

Mar 27,2025

UpStudy AI · Accepted Answer

1. Consider the transformation given by
   $$
   y = \frac{1}{x}.
   $$

2. For larger values of $$ x $$:
   - As $$ x $$ increases, $$ \frac{1}{x} $$ decreases and changes very little. For example, when $$ x $$ goes from 100 to 101:
     $$
     \frac{1}{100} = 0.01 \quad \text{and} \quad \frac{1}{101} \approx 0.0099.
     $$
   - The difference between these transformed values is quite small, implying that high $$ x $$ values are "compressed."

3. For smaller values of $$ x $$:
   - As $$ x $$ decreases, $$ \frac{1}{x} $$ increases and small changes in $$ x $$ lead to relatively larger changes in the transformed values.

4. Thus, the transformation compresses the range of high $$ x $$ values while stretching the range of low $$ x $$ values.

5. The statement that correctly completes the sentence "The effect of a $$ \frac{1}{x} $$ transformation is to ..." is:

$$
   \boxed{\text{compress the higher } x \text{ values in the data.}}
   $$

So, the correct answer is D.
The $$ \frac{1}{x} $$ transformation compresses the higher $$ x $$ values in the data.

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