Power function

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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.

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