2021 Fall AMC 10A Problems/Problem 16
Problem
The graph of is symmetric about which of the following? (Here is the greatest integer not exceeding .)
Solution 1 (Graphing)
Let and Note that the graph of is a reflection of the graph of about the -axis, followed by a translation of unit right.
The graph of is shown below: The graph of is shown below: The graph of is shown below:
Therefore, the graph of is symmetric about
~MRENTHUSIASM
Solution 2 (Piecewise Function)
For all real numbers and integers note that:
- and
We rewrite as We apply casework to the value of
Together, we have ..., so the graph of is symmetric about
IN PROGRESS AND WILL FINISH SOON. NO EDIT PLEASE. A MILLION THANKS.
~MRENTHUSIASM
See Also
2021 Fall AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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