Power Functions. Basics. Definition. A power function is a function of the form, f (x) = axp, where a ≠ 0 is a constant and p is a real number. Some examples of power functions include: Root functions, such as are examples of power functions.Graphically, power functions can resemble exponential or logarithmic functions for some values of x.he domain of a power function depends on the value of the power p. We will look at each case separately. 1. p is a non-negative integer. The domain is all real numbers (i.e. (− ∞,∞)). 2. p is a negative integer. The domain is all real numbers not including zero (i.e. (−∞, 0) ∪ (0,∞) or { x | x ≠ 0}).