Power Functions

A power function is a function where the variable has a power greater than one. Graphs of power functions will vary depending upon the value of the exponent.

Power functions have equations in the form: Power1-1. There are patterns in the shapes of the graphs of power functions. Power functions take two forms: Power1-2 and Power1-3. All power functions with even powers will graph similar to Power1-4 and power functions with odd powers will graph similar to Power1-5.

See the table and graph of two basic power functions below.





power_table

f(x) = x2 g(x) = x3

Graph1


Here are some situations that can be modeled by power functions:

  • Area (area vs. length).
  • Volume (volume vs. length).
  • A falling object (height vs. time).

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