Main Concept

Power functions of the form  $f\left(x\right)\=x^a$ are basic functions from which many other functions can be derived by applying transformations. For example, the function $f\left(x\right)\=x^2-4\cdot x\+7$ can be rearranged to the form $f\left(x\right)\={\left(x-2\right)}^2\+3$. The associated graph is the graph of  $x^2$ shifted to the right 2 units and up 3 units.

Some of the most common power functions are: the constant function $f\left(x\right)\=1$, ($a\=0$) the identity function $f\left(x\right)\=x$, the quadratic function $f\left(x\right)\=x^2$, the cubic function $f\left(x\right)\=x^3$, the square root function $f\left(x\right)\=\sqrt{x}$ , the cube root function $f\left(x\right)\=\sqrt[3]{x}$, the reciprocal function $f\left(x\right)\=\frac{1}{x}$ and the reciprocal of the quadratic function $f\left(x\right)\=\frac{1}{x^2}$.

$$ConstantFunctionIdentityFunctionQuadraticFunctionCubicFunctionSquareRootFunctionCubeRootFunctionReciprocalFunctionReciprocalSquared

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