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Difference between revisions of "2021 Fall AMC 10A Problems/Problem 16"
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==Problem==
 
The graph of <math>f(x) = |\lfloor x \rfloor| - |\lfloor 1 - x \rfloor|</math> 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 <math>f(x) = |\lfloor x \rfloor| - |\lfloor 1 - x \rfloor|</math> 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> the <math>y</math>-axis <math>\qquad \textbf{(B) }</math> the line <math>x = 1</math> <math>\qquad \textbf{(C) }</math> the origin <math>\qquad
 
<math>\textbf{(A) }</math> the <math>y</math>-axis <math>\qquad \textbf{(B) }</math> the line <math>x = 1</math> <math>\qquad \textbf{(C) }</math> the origin <math>\qquad
 
\textbf{(D) }</math> the point <math>\left(\dfrac12, 0\right)</math> <math>\qquad \textbf{(E) }</math> the point <math>(1,0)</math>
 
\textbf{(D) }</math> the point <math>\left(\dfrac12, 0\right)</math> <math>\qquad \textbf{(E) }</math> the point <math>(1,0)</math>
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==Solution==
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<b>IN PROGRESS AND WILL FINISH SOON. NO EDIT PLEASE. A MILLION THANKS.</b>
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~MRENTHUSIASM
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2021 Fall|ab=A|num-b=15|num-a=17}}
 
{{AMC10 box|year=2021 Fall|ab=A|num-b=15|num-a=17}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 23:34, 24 November 2021

Problem

The graph of $f(x) = |\lfloor x \rfloor| - |\lfloor 1 - x \rfloor|$ is symmetric about which of the following? (Here $\lfloor x \rfloor$ is the greatest integer not exceeding $x$.)

$\textbf{(A) }$ the $y$-axis $\qquad \textbf{(B) }$ the line $x = 1$ $\qquad \textbf{(C) }$ the origin $\qquad \textbf{(D) }$ the point $\left(\dfrac12, 0\right)$ $\qquad \textbf{(E) }$ the point $(1,0)$

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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