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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1} ).

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = kx^p }

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} are real numbers, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = f(x) } , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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