Question

Draw the graph of `f(x) ={2x}`, where `{*}` represents the fractional part function.

Answer 1

We have `f(x) = {2x}=2x- [2x]`
`" "={{:(......,,), (......,,),(2x+1",",,2x in [-1, 0) or x in [-1//2, 0)),(2x",",, 2x in [0, 1) or x in [0, 1//2)), (2x-1",",,2x in [1, 2) or x in [1//2, 1)), (2x-2",",, 2x in [2, 3) or x in [ 1, 3//2)),(2x-3",",,2x in [3, 4) or x in [3//2, 2)), (......,,),(......,,):}`
Thus, the graph is as shown in the following figure.