We need to first find the intervals where `x^(3)-x gt 0 and x^(3) -x lt 0`.
Now `" "x^(3) -x = x(x-1)(x+1)`
The sign scheme of `x^(3) -x ` is as shown in the following figure.
From the above sign scheme,
`" "y= f(x) = "sgn"(x^(3) - x)`
`" "= {{:(1",",, x in (-1, 0) uu (1, oo)), (-1",",, x in (-oo, -1)uu (0, 1)), (0",",, x=0"," pm 1):}`
Hence the graph of `f(x) = "sgn"(x^(3)-x)` is as shown in the following figure.
