What are Power Functions? | Functions and Relations, Types of Functions

What are power functions? Power functions are functions of the form f(x) = kx^a where k and a are both constant real numbers. So, in a power function, the variable is raised to a power. Other definitions restrict the coefficient k to being equal to 1, but that definition seems less common and does not describe a family of functions as useful in reality. We go over the definition of power functions and some examples and interesting properties in today's full math video lesson!

All power functions with positive even exponents have a parabolic shape, and if they have a coefficient of 1 they will intersect the points (1,1) and (-1,1). There are lots of interesting properties of power functions depending on their exponents and coefficients, try to figure some out on your own, and why the properties exist!

You also might notice, if you know what odd and even functions are, that power functions with even exponents are even functions, and power functions with odd exponents are odd functions! That's where "odd" and "even" functions get their name!

Desmos Graphing Software: https://www.desmos.com


I hope you find this video helpful, and be sure to ask any questions down in the comments!

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