Power function

For the Lego Technic motor system, see Lego Technic § Power Functions.

Power functions with $r=1,3$ and 5.

Power functions with $r=2,4$ and 6.

In mathematics, a power function is a function of the form :$f\colon x \mapsto c x^r \; c,r \in \mathbb{R}$ where $c$ and $r$ are constant real numbers and $x$ is a variable. The domain of a power function can sometimes be all real numbers, but generally a non-negativity $x \ge 0$ is used to avoid problems with simplifying. The domain of definition is determined by each individual case.

Power functions are a special case of power law relationships, which appear throughout mathematics and statistics.

See also

• Exponentiation