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2021 AMC 10C Question 16

AMC10 · 2021 AMC 10C

Question 16

Consider the function

$$
f(x) = |\lfloor x \rfloor| - |\lfloor 1 - x \rfloor|
$$

Its graph is symmetric about which of the following? (Here $\lfloor x \rfloor$ is the greatest integer not exceeding $x.$)
  1. the $y$-axis
  2. the line $x=1$
  3. the origin
  4. the point $\left(\dfrac{1}{2},0\right)$
  5. the point $(1,0)$