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Which of the following functions is the result of the reciprocal parent function undergoing a horizontal compression and a reflection across the -axis?
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Ask by Watson Pearson. in the United States
Mar 17,2025

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Tutor-Verified Answer

Answer

The correct function is .

Solution

The reciprocal parent function is
A reflection across the -axis changes to , so the function becomes
A horizontal compression by a factor of (with for compression) replaces with . Therefore, applying a horizontal compression and the -axis reflection yields
We compare this with the given options. Notice that in option (2), the function is
This shows a horizontal compression by a factor of 15 (since ) along with a reflection across the -axis.
Thus, the correct answer is

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Beyond the Answer

To determine which function results from the reciprocal parent function undergoing a horizontal compression and a reflection across the -axis, we can start with the standard reciprocal function .
When you reflect this function across the -axis, it becomes . A horizontal compression by a factor of modifies it to . Therefore, if the factor is , the new function will be .
So, the correct answer from the given options is:
.

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