Function `y=root(3)(x)`

Properties of the function `y=root(3)(x)`:

  1. Domain of the function is all number line, i.e. interval `(-oo,+oo)`.graph of the function y=root3(x)
  2. Function is odd: `f(-x)=root(3)(-x)=-root(3)(x)=-f(x)`.
  3. Function is increasing on all number line.

To draw graph of the function let's find some values of function for `x>=0`: if x=0, `y=root(3)(0)=0`; if x=1, `y=root(3)(1)=1`; if x=4, `y=root(3)(4)~~1.6`; if x=8, `y=root(3)(8)=2`.

Draw these points and then draw smooth curve through them. Now using the fact that this function is even, draw another part of graph symmetric about the origin. Result is shown on figure.