Power or polynomial function? According to the definition, $f(x) = a·x^n$ is a power function. If we shift it to $f(x) = a·(x - c)^n$ or, more general, to $f(x) = a·(x - c)^n + d$, it becomes a polynomial function (not a power function anymore). Is this just a matter of mere formalism or nomenclature?

Power functions must have a single term, but are allowed to have fractional or negative exponent.
Polynomials can have more than one term ("poly", meaning "many", refers to exactly this), but all exponents must be natural numbers.
A single term with a natural number exponent is both a power function and a polynomial (and actually a monomial) simultaneously.
