PPT-Section 2.7 (Part 1) Rational Functions

What is a rational function Definition A function of the form where and are polynomials and is not the zero polynomial What is the most common form of the equation   What does it look like. A Construction Using Fourier Approximations. UNIVERSALITY. To find one (or just a few) mathematical relationships (functions or equations) to describe a certain connection between ideas. .. Examples of this are common in science. Debdeep. . Mukhopadhyay. Associate Professor. Dept. of Computer . Sc. and . Engg. , . IIT . Kharagpur. Global Definitions. For a field K, n. ϵ. N, k. ϵ. K, we define:. . . n.k. =. Expression & Functions:. . Definitions, Multiplying, Dividing. Fractions - a Quick Review. Definitions. : . Rational . Functions, Expressions. Finding the Domains . (and Exclusions) of Rational Functions. Optional Pre-Final Exam Review. 1 – Basic Algebra Review. 2 – Graphs & Equations of Lines. 3 – Solving Systems of Equations. 4 – Inequalities. 5 – Polynomials & Factoring. 6 – Rational Expressions & Functions. Evaluating Rational & Irrational Exponents. Graphing Exponential Functions . f(x) = a. x. Equations with . x. and . y. Interchanged. Applications of Exponential Functions. Use calculators to calculate graphing points. Inverse variation. Recall: variables . x . and . y. show direct variation if . for some nonzero constant . a. .. *Note: the general equation . for inverse variation can be rewritten as . ..  . Classifying direct/inverse variation. Multiplying and Dividing. Definition of Rational Expressions . A rational expression is the ratio of two polynomials with the denominator not equal to 0. . For example. are rational expressions.. Domain. Functions. Section 7.1. The Logarithm . Defined as . an Integral. Section 7.2. Exponential Change and Separable Differential Equations. Section 7.3. Hyperbolic Functions. Section 7.4. Functions. Section 7.1. The Logarithm . Defined as . an Integral. Section 7.2. Exponential Change and Separable Differential Equations. Section 7.3. Hyperbolic Functions. Section 7.4. Functions. Defn. : . Rational . F. unction. A function in the form: .  . The functions . p. and . q. are polynomials.. The domain of a rational function is the set of all real numbers except those values that make the denominator, q(x), equal to zero.. Defn. : . Polynomial function. In the form of: . ..  . The coefficients are real numbers.. The exponents are non-negative integers.. The domain of the function is the set of all real numbers.. Rational Equations and Functions Algebra II Chapter 8 This Slideshow was developed to accompany the textbook Larson Algebra 2 By Larson , R., Boswell, L., Kanold , T. D., & Stiff, L. 2011 Holt Writing Rational Functions Honors Algebra II Keeper Think Backwards!!! Example: Write a rational function f that has a vertical asymptote at , a horizontal asymptote and a zero at .   Example: Write a rational function g with vertical asymptotes at DRAFT 2018Algebra 2Page1Algebra 2and Mathematics 3 Critical Areas of FocusOhios Learning Standards for Mathematics include descriptions of the Conceptual Categories These descriptions have been used t