The function is considered for all real numbers

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

Problem

The function

p(x)=\lfloor x\rfloor+\operatorname{sgn}(x)

is considered for all real numbers

x\in(-5,5)

. How many distinct integer values can

p(x)

take? (a) 8 (b) 10 (c) 11 (d) 9