The concept of a power function with a natural, integer and rational exponent

Power function

A power function has the form $y=x^p$ , where $p$ is a fixed number (the exponent) and $x$ is the independent variable. Depending on the set $p$ belongs to, we speak of a power function with natural, integer, or rational exponent. Each case needs a careful domain

D(y)

: e.g. for fractional $p$ negative $x$ are often excluded until complex numbers appear.

All graph geometry depends on which exponent

p

is fixed in the formula

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