Question

Draw the graph of the fractional part function:
`f:RtoR:f(x)=x-[x]=[x]`

Answer 1

We have, `f(3)=0,f(3.1)=0.1,f(3.2)=0.2,......,f(3,9)=0.9,f(4)=0`.
`f(2)=0,f(2.1)=0.1,f(2.2)=0.2,......,f(2.9),=0.9,f(3)=0`.
`f(1)=0,f(1.1)=0.1,f(1.2)=0.2,......,f(1.9)=0.9,f(2)=0`.
`f(0)=0,f(0.1)=0.1,f(0.2)=0.2,......,f(0.9)=0.9,f(1)=0`.
`f(-1)=0,f(-0.9)=0.1,f(-0.8)=0.2,......,f(-0.1)=0.9,f(0)=0`.
`f(-2)=0,f(-1.9)=0.1,f(-1.8)=0.2,......,f(-1.1)=0.9,f(-1)=0`
`f(-3)=0,f(-2.9)=1.0,f(-2.8)=0.2,......,f(-2.1)=0.9,f(-2)=0`.
Plotting these points on a graph paper, we may get the graph as shown below.