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Learn what a rational function is, how to write it as a ratio of two polynomials, and how to identify its asymptotes. See how to transform rational functions using the general formula and examples.

https://math.libretexts.org › Bookshelves › Algebra › Intermediate_Algebra_(Arnold) › 07...

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://math.libretexts.org › Bookshelves › Precalculus › Precalculus_(Stitz-Zeager) › 04...

A rational function is a function which is the ratio of polynomial functions. Said differently, r is a rational function if it is of the form. r(x) = p(x) q(x), where p and q are polynomial functions. a. a According to this definition, all polynomial functions are also rational functions. (Take q(x) = 1).

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

rational function: Any function whose value can be expressed as the quotient of two polynomials (where the polynomial in the denominator is not zero). singularities: The [latex]x[/latex]-values at which a rational function is not defined, for which the denominator [latex]Q(x)[/latex] is zero.

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

Learn how to use arrow notation, solve applied problems, find domains, and graph rational functions. See examples of vertical and horizontal asymptotes, and how to identify them from the function rule.

https://mathmonks.com › rational-function

The word ‘ratio’ is the root of the term ‘rational’. Thus, a rational function is the ratio of two polynomial functions where the denominator is never 0. A function of a real variable x, say f (x), is a rational function if it can be represented as: f (x) = p (x) q (x), here p (x), q (x) are polynomials in x with q (x) ≠ 0.

https://www.symbolab.com › ... › collegealgebra2017 › introduction-rational-functions.html

Rational Functions. Suppose we know that the cost of making a product is dependent on the number of items, x, produced. This is given by the equation C\left (x\right)=15,000x - 0.1 {x}^ {2}+1000 C (x) = 15,000x −0.1x2 + 1000. If we want to know the average cost for producing x items, we would divide the cost function by the number of items, x.