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Definition: Rational Functions. A rational function is a function that can be written as a quotient of two polynomial functions. In symbols, the function \[f(x)=\frac{a_{0}+a_{1} x+a_{2} x^{2}+\cdots+a_{n} x^{n}}{b_{0}+b_{1} x+b_{2} x^{2}+\cdots+b_{m} x^{m}} \nonumber \] is called a rational function.

https://www.cuemath.com › calculus › rational-function

Learn what a rational function is, how to identify it, and how to graph it. Find out the domain, range, and asymptotes of a rational function with examples and practice problems.

https://www.symbolab.com › study-guides › boundless-algebra › rational-functions.html

Any function of one variable, [latex]x[/latex], is called a rational function if, and only if, it can be written in the form: [latex-display]f(x) = \dfrac{P(x)}{Q(x)}[/latex-display] where [latex]P[/latex] and [latex]Q[/latex] are polynomial functions of [latex]x[/latex] and [latex]Q(x) \neq 0[/latex]. Note that every polynomial function is a ...

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Learn how to simplify, add, subtract, multiply and divide rational functions, which are fractions with polynomials as numerators and denominators. See examples, graphs and step-by-step guides for each operation.

https://www.math.net › rational-function

A rational function is a function made up of a ratio of two polynomials. Learn how to identify and transform rational functions, and what are vertical and horizontal asymptotes.

https://math.libretexts.org › Courses › Cosumnes_River_College › Math_370:_Precalculus › 04...

Learn how to define, simplify, and graph rational functions, which are ratios of polynomial functions. See examples of finding the domain, writing in the form \\frac {p (x)} {q (x)}, and identifying horizontal and slant asymptotes.