AdvancedProPower Functions
Fractional Power
f(x) = ax^(p/q)
Overview
Fractional exponents represent roots. x^(1/2) = √x, x^(1/3) = ∛x, etc.
Domain
x ≥ 0 (even q) or all reals (odd q)
Range
Depends on p/q
Symmetry
Depends on q
Key Properties
1
p/q exponent = q-th root of x^p
2
Even q → domain restricted to x ≥ 0
3
Odd q → defined for all real x
4
Vertical tangent at x = 0 when p/q < 1
Key Insight
x^(2/3) = (x^(1/3))² — always non-negative, defined for all x. A classic example of a fractional power.
Visualize Fractional Power
Interact with the graph, adjust parameters, and see how the function behaves in real time.