Question
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
graph of
(1) Shift down 8 units
(2) Rellect about the
(3) Reflect about the
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.
-
Shift down 8 units:
- Shifting a function down by
units involves subtracting from the function. - For
, shifting down 8 units gives us:
- Shifting a function down by
-
Reflect about the
-axis: - Reflecting a function about the
-axis involves multiplying the entire function by -1. - Applying this to
results in:
- Reflecting a function about the
-
Reflect about the
-axis: - Reflecting a function about the
-axis involves replacing with in the function. - Applying this to
gives us:
- Reflecting a function about the
Thus, the final function after applying all the transformations is:
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Beyond the Answer
To start, we take the basic function
.
- Shift down 8 units: The function after this transformation becomes
. - Reflect about the
-axis: This flips the function over the -axis, resulting in or . - 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!