Question
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Find the function that is finally graphed after the following transformations are applied to the
graph of in the order listed.
(1) Shift down 8 units
(2) Rellect about the -axis
(3) Reflect about the -axis

Ask by Bush Savage. in the United States
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The final function after the transformations is .

Solution

To find the function that results from the given transformations applied to the graph of , we will go through each transformation step by step.
  1. Shift down 8 units:
    • Shifting a function down by units involves subtracting from the function.
    • For , shifting down 8 units gives us:
  2. Reflect about the -axis:
    • Reflecting a function about the -axis involves multiplying the entire function by -1.
    • Applying this to results in:
  3. Reflect about the -axis:
    • Reflecting a function about the -axis involves replacing with in the function.
    • Applying this to gives us:
Thus, the final function after applying all the transformations is:

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

Beyond the Answer

To start, we take the basic function .
  1. Shift down 8 units: The function after this transformation becomes .
  2. Reflect about the -axis: This flips the function over the -axis, resulting in or .
  3. Reflect about the -axis: This reflection transforms the function to .
In conclusion, after applying all transformations, the final function is:
So, the function graphed has been dramatically transformed into a reflection and shift resultant from your given steps!

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