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2021 AMC Fall 10A Problem 16

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2021 AMC Fall 10A Problem 16AMC 10 Step by Step

Name: Date: September 13, 2026

Functions · difficulty 3 of 5 · about 4 min · position P16-20

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 $x$ .)

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

2021 AMC Fall 10A Problem 16

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