Power Function with Positive Fractional Exponent

Consider function `y=x^r`, where r is positive irreducible fraction.

Properties of this function are following:graph of the function with positive fractional exponent

  1. Domain is interval `[0,+oo)`.
  2. Function is neither even, nor odd.
  3. Function is increasing on interval `[0,+oo)`.

On the left figure is drawn graph of the function `y=x^(5/2)`. It is located between graphs of the function `y=x^2` and `y=x^3`, defined on interval `[0,+oo)`. Similar form has any graph of the function `y=x^r`, where `r>1`.

On the right figure is draw graph of the function `y=x^(2/3)`. Similar form has any graph of the function `y=x^r`, where `0<r<1`.