Let the function be defined by .

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let the function

f:\,[-3,4)\to\mathbb R

be defined by

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

. (i) Compute

f(-2.7),\;f(-1),\;f(0),\;f(2.3)

and

f(3.9)

. (ii) Determine the range of

f

on the given domain

[-3,4)

. (iii) Verify that every element of the range found in part (ii) is actually attained by some

x

[-3,4)