2021 Fall AMC 10A Problems/Problem 16

Revision as of 00:42, 23 November 2021 by Mop (talk | contribs) (Created page with "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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 $(1,0)$