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History1979TEXandMETAFONTKnuth19862DBeziercontrolpointselectionHobby1989MetaPostHobby2004Asymptote2004initialpublicreleaseHammerlindlBowmanPrince20053DBeziercontrolpointselect. Describe the end behavior of:. Graph the function. Determine the interval(s) on which the function is increasing and on which it is decreasing. . Lesson 3-7 Graphs of Rational Functions. Objective: 1. To graph rational functions.. 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!!. AII.7 e . 2009. Objectives:. Find the Vertical Asymptotes. Find the Horizontal Asymptotes. Rational . Functions . A rational function can have more than one . vertical asymptote. , but it can have at most one . Harmonic Oscillator. Our next model is the quantum mechanics version of a spring:. Serves as a good model of a vibrating (diatomic) molecule . The simplest model is a . harmonic oscillator. :. Harmonic Oscillator. Graphing Rational Functions. If the . degree of the numerator is greater than the degree of the denominator by 1. , then there is not a horizontal asymptote, but an oblique one. The equation is found by doing long division and . Vertical Asymptotes (VA). If . then . x=a is a VA of f(x. ). To find VA algebraically – set denominator = 0. Example 1 – Find VA. Finding limits on either side of a VA. Unit . 3. Polynomial Functions. Section: . 5.1. Polynomial Functions . This section studies the . Polynomial Function. .. Your Goal - learn to . identify. the function components that lead to its . . – . The Graph of a Rational . Function. 3 examples. General Steps to Graph a Rational Function. 1) Factor the numerator and the denominator. 2) State the domain and the location of any holes in the graph. x-intercepts:. an x-intercept is any x-value whose y-value. Write answer as . y. -intercept. A y-intercept is any y-value whose x-value. Write answer as .  . Find the x-intercept and the y-intercept. What happens as . x. gets large? How could we express this as a limit?. Notice that y = 2 is a horizontal asymptote!. As the denominator gets larger, the value of the fraction gets smaller.. If then . 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.. Definition of a Vertical Asymptote. If f(x) approaches ±∞ as x approaches c from the left or right, then the line x = c is a . vertical asymptote. .. Vertical Asymptotes can be determined by finding where there is . Chapitre 3: Les fonctions rationnelles MHF4U 3.1: L’inverse d’une fonction affine Comment décrire la fonction suivante? Vocabulaire * Hyperbole : Courbe avec points pour lesquels la différence de distance à 2 points fixes (foyers) est égale. 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