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Concept

Power Function

A power function is a polynomial function that consists of a variable base raised to a fixed power. It can always be written in the following form.

$y = a \cdot x^{b}$

Here,

a

and

b

are real numbers. Now, consider a few graphs of power functions.

Note that a constant function, identity function, quadratic function, cubic function, reciprocal function, cube root function are all examples of power functions as they can be expressed in the given form.

Function	Equation	Power Function Form
Constant Function	$y = 7$	$y = 7 x^{0}$
Identity Function	$y = x$	$y = x^{1}$
Quadratic Function	$y = 3 x^{2}$	$y = 3 x^{3}$
Cubic Function	$y = 0.5 x^{3}$	$y = 0.5 x^{3}$
Reciprocal Function	$y = \frac{1}{x}$	$y = x^{- 1}$
Cube Root Function	$y = 2 3 x$	$y = 2 x^{\frac{1}{3}}$

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