Question

Identify the range of the greatest integer function $y=\left[[x-3]\right]$ for $-3<x<3$

• A. $-5<x<0$
• B. $-6<x<0$
• C. $-7<x<-1$
• D. $x=-6,-5,-4,-3,-2,-1,0$
• E. $x=-6,-5,-4,-3,-2,-1$

Answer 1

The correct option is E $x=-6,-5,-4,-3,-2,-1$

Given, $-3<x<3$, which implies $-6<x-3<0$
Given, $y=[x-3]$, since $-6<x-3<0$

The values taken by $y$ are $-6,-5,-4,-3,-2,-1$
Therefore, the range of the function is $-6,-5,-4,-3,-2,-1$.