Question

Sketch the graph of the function defined by $f\left(x\right)=\left[x\right],x\in [-3,3]$ and find its range.

Answer 1

$f\left(x\right)=\left[x\right],x\in [-3,3]$

$f\left(x\right)=-3$, for, $x\in [-3,-2)$

$f\left(x\right)=-2$, for, $x\in [-2,-1)$

$f\left(x\right)=-1$, for, $x\in [-1,0)$

$f\left(x\right)=0$, for, $x\in [0,1)$

$f\left(x\right)=1$, for, $x\in [1,2)$

$f\left(x\right)=2$, for, $x\in [2,3)$

$f\left(x\right)=3$, for, $x=3$

Range $=\{-3,-2,-1,0,1,2,3\}$