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- https://math.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/College_Algebra_(NWTC)/04%3A_Rational_and_Radical_Functions/4.01%3A_Rational_FunctionsIn this section, we explore functions based on power functions with negative integer powers, called rational functions.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_(Arnold)/07%3A_Rational_Functions/7.03%3A_Graphing_Rational_FunctionsWe’ve seen that the denominator of a rational function is never allowed to equal zero; division by zero is not defined. So, with rational functions, there are special values of the independent variabl...We’ve seen that the denominator of a rational function is never allowed to equal zero; division by zero is not defined. So, with rational functions, there are special values of the independent variable that are of particular importance. Now, it comes as no surprise that near values that make the denominator zero, rational functions exhibit special behavior, but here, we will also see that values that make the numerator zero sometimes create additional special behavior in rational functions.
- https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Precalculus__An_Investigation_of_Functions_(Lippman_and_Rasmussen)/03%3A_Polynomial_and_Rational_Functions./3.07%3A_Rational_FunctionsIn this section, we explore functions based on power functions with negative integer powers, called rational functions.
- https://math.libretexts.org/Workbench/Hawaii_CC_Intermediate_Algebra/06%3A_Polynomial_and_Rational_Functions/6.06%3A_Rational_Functions_-_Addition_and_SubtractionAdding and subtracting rational expressions is similar to adding and subtracting fractions. Recall that if the denominators are the same, we can add or subtract the numerators and write the result ove...Adding and subtracting rational expressions is similar to adding and subtracting fractions. Recall that if the denominators are the same, we can add or subtract the numerators and write the result over the common denominator. When working with rational expressions, the common denominator will be a polynomial.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.06%3A_Limits_at_Infinity_and_Asymptotes/4.6E%3A_Exercises_for_Section_4.6This page offers exercises on identifying and evaluating vertical and horizontal asymptotes in mathematical functions and limits. It provides graphs showcasing asymptotic behavior, calculations for de...This page offers exercises on identifying and evaluating vertical and horizontal asymptotes in mathematical functions and limits. It provides graphs showcasing asymptotic behavior, calculations for determining the presence of asymptotes, and evaluations of limits as \(x\) approaches extreme values. The text discusses properties of various functions, including local maxima, minima, and inflection points, while outlining conditions for asymptote definitions.
- https://math.libretexts.org/Courses/Clovis_Community_College/Precalculus%3A__Describing_Relationships_Between_Quantities_in_the_World_Around_Us/04%3A_Polynomial_and_Rational_Functions./4.06%3A_Rational_FunctionsIn this section, we explore functions based on power functions with negative integer powers, called rational functions.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/04%3A_Polynomial_and_Rational_Functions/405%3A_Rational_Functions__Multiplication_and_DivisionRational functions have the form r(x)= p(x)/q(x) , where p(x) and q(x) are polynomials and q(x)≠0. Simplifying rational expressions is similar to simplifying fractions.
- https://math.libretexts.org/Workbench/Hawaii_CC_Intermediate_Algebra/06%3A_Polynomial_and_Rational_Functions/6.05%3A_Rational_Functions_-_Multiplication_and_DivisionRational functions have the form r(x)= p(x)/q(x) , where p(x) and q(x) are polynomials and q(x)≠0. Simplifying rational expressions is similar to simplifying fractions.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/04%3A_Polynomial_and_Rational_Functions/406%3A_Rational_Functions__Addition_and_SubtractionAdding and subtracting rational expressions is similar to adding and subtracting fractions. Recall that if the denominators are the same, we can add or subtract the numerators and write the result ove...Adding and subtracting rational expressions is similar to adding and subtracting fractions. Recall that if the denominators are the same, we can add or subtract the numerators and write the result over the common denominator. When working with rational expressions, the common denominator will be a polynomial.
- https://math.libretexts.org/Courses/North_Hennepin_Community_College/Math_1120%3A_College_Algebra_(Lang)/02%3A_Polynomial_and_Rational_Functions./2.07%3A_Rational_FunctionsIn this section, we explore functions based on power functions with negative integer powers, called rational functions.