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. Remember to Silence Your Cell Phone and Put It In Your Bag!. Comparing Rational Numbers (in fraction form). Models. For , where b>0, iff a<c.. For , where b>0 and d>0, . 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. Rational Numbers. The . real number system. consists of rational and irrational numbers.. . Rational numbers. can be expressed in fractional form, , where a (the numerator) and b (the denominator) are both integers and b = 0.. 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. The word . rational. contains the word . ratio. , which is another word for quotient. A rational number can be written as a ratio of integers.. Example 1 – . Determining Whether Numbers Are Rational or Irrational. Subtitle. Finding a Common Denominator. Adding and subtracting rational numbers with variables works much the same way as constants. The only variations we need to worry about is how to handle multiplication by variable factor and how that factor affects the numerator’s sum or difference.. , . are.  . canonical.  solutions . y. (. x. ) of . Bessel's . differential equation. :. α (the . order.  of the Bessel function). Bessel functions are also known as . cylinder functions.  or . 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. Dr Brian O’ Boyle . St Angela’s College . S. ligo. Elasticity. How would we expect a student to answer to the following question. Explain in your own words what elasticity means?. Elasticity – Application of Rational Choice. Dr Jane Robertson. Policy, Access and Use Team, EMP. 4 November 2014. Appropriate use of medicines. Relies on a number of elements. Availability. , . affordability, and use in practice of effective medicines.