For , find the range of…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

For

-3<x\le 4

, find the range of

g(x)=2\,\bigl\lfloor \tfrac{x}{2}\bigr\rfloor-\mathrm{sgn}(x)

. (a)

\{-3,-1,1,3\}

(b)

\{-3,-2,-1,0,1,3\}

(c)

\{-3,-1,0,1,3\}

(d)

\{-4,-2,0,2,4\}