Difference between revisions of "2021 Fall AMC 10A Problems/Problem 16"
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The graph of <cmath>f(x) = |\lfloor x \rfloor| - |\lfloor 1 - x \rfloor|</cmath> is symmetric about which of the following? (Here <math>\lfloor x \rfloor</math> is the greatest integer not exceeding <math>x</math>.) | The graph of <cmath>f(x) = |\lfloor x \rfloor| - |\lfloor 1 - x \rfloor|</cmath> is symmetric about which of the following? (Here <math>\lfloor x \rfloor</math> is the greatest integer not exceeding <math>x</math>.) | ||
| − | <math>\textbf{(A) } | + | <math>\textbf{(A) }\text{the }y\text{-axis}\qquad \textbf{(B) }\text{the line }x = 1\qquad \textbf{(C) }\text{the origin}\qquad |
| − | \textbf{(D) } | + | \textbf{(D) }\text{ the point }\left(\dfrac12, 0\right)\qquad \textbf{(E) }\text{the point }(1,0)</math> |
==Solution== | ==Solution== | ||
Revision as of 23:44, 24 November 2021
Problem
The graph of ![\[f(x) = |\lfloor x \rfloor| - |\lfloor 1 - x \rfloor|\]](http://latex.artofproblemsolving.com/0/8/5/0856042a755ebc88c0261897b7fad311209d9e99.png)
is symmetric about which of the following? (Here 
is the greatest integer not exceeding 
.)
Solution
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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