Graphing Overview
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: . There are patterns in the shapes of the graphs of power functions. Power functions take two forms:
and
. All power functions with even powers will graph similar to
and power functions with odd powers will graph similar to
.
See the table and graph of two basic power functions below.
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f(x) = x2 g(x) = x3
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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).