Power Function with Negative Fractional Exponent

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

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

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

On the figure is shown graph of the function `y=x^(-1/2)`. Similar for has graph of any function `y=x^r`, where r is negative fraction.