Power functions with natural numbers as exponent

A power function with a natural as exponent is a function of the form $f(x)=a\cdot x^n$ ($n\in \mathbb{N},a\in ℝ$)

The form of the power function depends on the exponent $n$ and on the coefficient $a$.

Example

The volume of a sphere with radius r is given by the expression $V(r)=\frac{4}{3}\pi \cdot r^3$. Here, $V(r)$ is a power function with exponent 3 and coefficient $\frac{4}{3}\pi$.