Power functions of the form fx=xa are basic functions from which many other functions can be derived by applying transformations. For example, the function fx=x2−4⋅x+7 can be rearranged to the form fx=x−22+3. The associated graph is the graph of x2 shifted to the right 2 units and up 3 units.
Some of the most common power functions are: the constant function fx=1, (a=0) the identity function fx=x, the quadratic function fx=x2, the cubic function fx=x3, the square root function fx=x , the cube root function fx=x3, the reciprocal function fx=1x and the reciprocal of the quadratic function fx=1x2.
Examine the graphs and properties of some elementary functions.
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