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Power functions of the form are basic functions from which many other functions can be derived by applying transformations. For example, the function can be rearranged to the form . The associated graph is the graph of shifted to the right 2 units and up 3 units.
Some of the most common power functions are: the constant function , () the identity function , the quadratic function , the cubic function , the square root function , the cube root function , the reciprocal function and the reciprocal of the quadratic function .
Examine the graphs and properties of some elementary functions.
This function has a y-intercept at (0,1) and no x-intercept.
It is neither increasing nor decreasing - it is a constant function.
It is an even function, so it is symmetric about the y-axis.
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