Difference between revisions of "2021 Fall AMC 10A Problems/Problem 16"
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<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> | ||
| + | |||
| + | == Solution 1 == | ||
| + | Since <math>f(1-x)=|\lfloor 1-x \rfloor|-|\lfloor x \rfloor|=-f(x)</math>, <math>f(x)</math> is symmetric about the point <math>\left(\dfrac12, 0\right)</math> | ||
| + | <math>\box{\textbf{(D) } } \text{the point} \left(\dfrac12, 0\right)</math> | ||
Revision as of 12:06, 23 November 2021
The graph of 
is symmetric about which of the following? (Here 
is the greatest integer not exceeding 
.)
the 
-axis 
the line 
the origin 
the point 
the point 
Solution 1
Since 
, 
is symmetric about the point
$\box{\textbf{(D) } } \text{the point} \left(\dfrac12, 0\right)$ (Error compiling LaTeX. Unknown error_msg)
