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Theory

Take a look at the applet: Power Functions

A power function is a function of the form f ( x ) = a ( x + b ) p + c , where p can also take any real value. This sort of function is derived by transformation from y = x p . A few examples:

  • p = 0 :
    f ( x ) = a + c a constant function.

  • p = 1 :
    f ( x ) = a x + d a linear function.

  • p = 2 :
    f ( x ) = a ( x + b ) 2 + c a quadratic function.

  • p = 1 2 :
    f ( x ) = a ( x + b ) 1 2 + c = a x + b + c a radical function.

  • p = -1 :
    f ( x ) = a ( x + b ) -1 + c = a x + b + c a hyperbolic function.

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