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2B. Power Functions

Autor:Will McGuffey

Instructions:

  • Use the input box or slider tools for and to set the values of the coefficient and power, respectively.
  • Use the input box for and slider tool for to set the locations of the points and on the graph to visualize the rate of change of the power function at different points on its graph.

Power Functions

Power functions have the form , where is a constant called the coefficient and is a constant power. The power determines the shape of the graph. There are several categories of power functions with similar graph shapes.
  • When n is a positive, odd integer (e.g., ).
  • When n is a positive, even integer (e.g., ).
  • When n is a negative, odd integer (e.g., ).
  • When n is a negative, even integer (e.g., ).
  • When n is a fraction (e.g., ).
While the power gives the shape of the graph, the coefficient can stretch/shrink the graph vertically and reflect the graph across the -axis (if ).

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