PPT-Analyzing and sketching the graph of a rational function

25 Rational Functions Rational Functions A function of the form f x N x D x where N and D are both polynomials Examples What we will be doing Finding some characteristics of rational functions that will help us to be able to graph the function. 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. Precalculus. : Do Now. Graph the function below by hand. Be sure to factor the function, find the horizontal and vertical asymptotes, and the x and y-intercepts . Only use a graphing calculator at the very end to confirm your answer. REMEMBER FAITS!!. Why do we use the discriminant?. The discriminant tells us one of two things:. How many roots/x-intercepts/zeros does a quadratic function have?. How many solutions does a quadratic equation have?. Example. Expression & Functions:. . Definitions, Multiplying, Dividing. Fractions - a Quick Review. Definitions. : . Rational . Functions, Expressions. Finding the Domains . (and Exclusions) of Rational Functions. Functions. KFUPM - Prep Year Math Program (c) 20013 All Right Reserved. Domain . of a . Function . . Vertical Line Test . . Piecewise Function . Graphing a . function . KFUPM - Prep Year Math Program (c) 2009 All Right Reserved. Lesson 4-4. To graph a function rule:. Choose 3-5 numbers for x (unless the domain is given to you.). Complete a function table to find values for y.. Graph the resulting ordered pairs.. A. y = 2x + 4. Chapter 5.6. Review: Zeros of Quadratic Functions. In the previous chapter, you learned several methods for solving quadratic equations. If, rather than a quadratic equation . , we think about the function . 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. 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 4.5 beginning on page 190. Solving By Factoring. We already know how the zero product property allows us to solve quadratic equations, this property also allows us to solve factored polynomial equations [we learned how to factor polynomial expressions in the previous section].. 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 Robert Krauthgamer, . Weizmann Institute of Science. Bertinoro. . workshop, May . 2014. Joint work with . Alexandr. . Andoni. and David Woodruff. TexPoint. fonts used in EMF. . Read the . TexPoint.