Power Functions - Maple Programming Help

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Power Functions

 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 $f\left(x\right)=\frac{1}{{x}^{2}}$.

Examine the graphs and properties of some elementary functions.



 $f\left(x\right)=$ Properties:

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