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In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.
有理函數 （英語： Rational function ）是可以表示為以下形式的 函數 ： ， 不全為0。 有理數 式 是多項式除法的商，有時稱為 代數分數 。 漸近線. 不失一般性 可假設分子、分母 互質 。 若存在 ，使得 是分母 的因子，則有理函數存在垂直 漸近線 。
有理函數（英語： Rational function ）是可以表示為以下形式的函數： f ( x ) = a m x m + a m − 1 x m − 1 + ⋯ + a 1 x + a 0 b n x n + b n − 1 x n − 1 + ⋯ + b 1 x + b 0 = P m ( x ) Q n ( x ) ; m , n ∈ N 0 {\displaystyle f(x)={\frac {a_{m}x^{m}+a_{m-1}x^{m-1}+\cdots +a_{1}x+a_{0}}{b_{n}x^{n}+b_{n-1}x^{n-1}+\cdots ...
A rational function is a fraction of polynomials. Asymptotes play an important role in graphing rational functions. Learn how to find the domain and range of rational function and graphing it along with examples.
Divide one polynomial by another, and what do you get? A rational function! We'll analyze the family of rational functions, and we'll see some examples of how they can be useful in modeling contexts.
A rational function is a function that can be written as a quotient of two polynomial functions. In symbols, the function \[f(x)=\frac{a_{0}+a_{1} x+a_{2} x^{2}+\cdots+a_{n} x^{n}}{b_{0}+b_{1} x+b_{2} x^{2}+\cdots+b_{m} x^{m}} \nonumber \]
This topic covers: - Simplifying rational expressions - Multiplying, dividing, adding, & subtracting rational expressions - Rational equations - Graphing rational functions (including horizontal & vertical asymptotes) - Modeling with rational functions - Rational inequalities
