Power Functions with Any Exponent

(Video) Power Functions and Their Graphs

by ProfessorRosever

In this video by ProfessorRosever a power function is defined.

(Video) Power Functions and Their Properties

by Math Easy Solutions

In this video by Math Easy Solutions power functions are defined and their properties are described.

Power Functions

Power functions are functions that are raised to a power, $a$. $a$ is a constant. We have seen power functions before, such as with quadratic functions and cubic functions.

The general form is:

$$f(x) = cx^a$$

We've seen something that looks similar before, $f(x)=a^x$, which is an exponential function, where $x$ is raised to a constant value. Quadratic and cubic functions are also examples! You may also remember learning about functions where there is a variable base.

Typically, power functions go until infinity ($\rightarrow \infty$).

Even exponents, such as the quadratic function, are generally shaped like (the behavior of a power function is) a U. Think about the characteristics of exponents - even-powered functions negate any possible negative values. Odd exponents, such as the cubic function, follow the general shape of the cubic function.

It may help to practice graphing power functions to understand what they do. Different factors like when the coefficient is negative or if there is a fraction involved will affect how the power function looks.

In the next lessons, we will extend this topic to cover inverse powers and equations with powers.