PPT-Writing Rational Functions

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. A horizontal asymptote is a sp cial case of a slant asymptote recipe for find ing a horizontal asymptote of a rational function Let deg Nx the degree of a numerator and deg Dx the degree of a denominator deg Nx deg Dx deg Nx deg Dx deg Nx deg Dx 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. =. 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. 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.. Quadratic Function. A . quadratic function . is defined by a quadratic or second-degree polynomial.. Standard Form. , . where . a. . ≠ 0. .. Vertex Form. , where a. . ≠ 0..  . Vertex and Axis of Symmetry. 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?. Section 4.1. Polynomial Functions. Determine roots of polynomial equations. Apply the Fundamental Theorem of Algebra. Polynomial in one variable. A polynomial in one variable x, is an expression of the form a. Writing Generic Functions Lecture 20 Hartmut Kaiser hkaiser@cct.lsu.edu http://www.cct.lsu.edu/˜ hkaiser /spring_2015/csc1254.html Code Quality 3/26/2013 Lecture 18 CSC 1254, Spring 2015, Writing Generic Functions 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 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