Intro to Power Functions

A monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. For example, $x^{2}yz^{3}=xxyzzz$ is a monomial. The constant $1$ is a monomial, being equal to the empty rpdouct and to $x^{0}$ for any variable $x$. If only a single variable $x$ is considered, this means that a monomial is either $1$ or a power $x^{n}$ of $x$, with $n$ a positive integer. If several variables are considered, say, $x,y,z,$ then each can be given an exponent, so that any monomial is of the form $x^{a}y^{b}z^{c}$ with $a,b,c$ non-negative integers (taking note that any exponent $0$ makes the corresponding factor equal to $1$).

A power function is a function that can be represented in the form

$f(x)=kx^{p}$

where $k$ and $p$ are real numbers, and $k$ is known as the coefficient. We can also think of a power function as a monomial function; that is, a power function takes the form $y=f(x)$, where $f(x)$ is a single-variable monomial.

Resources

• Intro to Power Functions and Polynomial Functions, Book Chapter
• [https://openstax.org/books/college-algebra/pages/5-2-power-functions-and-polynomial-functions Power Functions and Polynomial Functions
• Guided Notes