4 Select the statement which correctly completes the sentence
“The effect of an 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 reverse the order of the values in the data

Ask by Cervantes Reed. in Australia

Mar 27,2025

Question

4 Select the statement which correctly completes the sentence
“The effect of an 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 reverse the order of the values in the data

Ask by Cervantes Reed. in Australia

Mar 27,2025

UpStudy AI · Accepted Answer

To determine the correct completion of the sentence "The effect of an $$ x^{2} $$ transformation is to ...", we need to analyze how squaring the values of $$ x $$ affects the data.

1. **Understanding the transformation**: When we apply the transformation $$ x^2 $$, all values of $$ x $$ are squared. This means:
   - Positive values of $$ x $$ become larger (e.g., $$ 2 $$ becomes $$ 4 $$).
   - Negative values of $$ x $$ also become larger in magnitude but positive (e.g., $$ -2 $$ becomes $$ 4 $$).
   - The value $$ 0 $$ remains $$ 0 $$.

2. **Effect on higher and lower values**:
   - Higher positive values are stretched further away from zero.
   - Lower negative values (which are also higher in terms of absolute value) are transformed into positive values, effectively compressing their original negative distance from zero.

Now, let's evaluate the options:
- **A**: Stretch the higher $$ x $$ values in the data - This is true, as higher positive values become larger.
- **B**: Maintain the distance between values - This is false, as the distances change.
- **C**: Stretch the lower $$ x $$ values in the data - This is misleading; lower values (negative) become positive but do not stretch in the same sense.
- **D**: Compress the higher $$ x $$ values in the data - This is false; higher values are stretched.
- **E**: Reverse the order of the values in the data - This is false; the order is not reversed.

Based on this analysis, the correct answer is:

**A**: stretch the higher $$ x $$ values in the data.
The correct statement is: A. stretch the higher $$ x $$ values in the data.

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