Question

Draw the graph of the greatest integer function:

$f:R\to R:f\left(x\right)=\left[x\right]$ for all $xϵR$

Answer 1

Using the definition of $\left[x\right]$, we have

$\left[x\right]=-2$, for $-2\le x<-1$

$\left[x\right]=-1$, for $-1\le x<0$

$\left[x\right]=0$, for $0\le x<1$

$\left[x\right]=1$, for $1\le x<2$

$\left[x\right]=2$, for $2\le x<3$

$\left[x\right]=3$, for $3\le x<4$.

Taking the scale: 10 small divisions = 1 unit, the graph of the function $f\left(x\right)=\left[x\right]$ may be drawn as shown below.