PDF-ASYMPTOTES OF RATIONAL FUNCTIONS where Nx and Dx are p

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. 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!!. 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, . 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 . Rational Number . Number that can be written as a fraction. -1/5 2 9/8 -6/3. Terminating Decimal . A decimal expansion that terminates in all 0’s. A TERMINATOR stops bugs. . A decimal that stops / ends. A bit more practice in Section 4.7b. Analysis of the Inverse Sine Function. 1. –1. D:. R:. Continuous. Increasing. Symmetry: Origin (odd . func. .). Bounded. Abs. Max. of at . x. = 1. Abs. Min. of at . . – . 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. 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. 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.. 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 . “Rational Choice” Theories and Situational Crime Prevention “Rational Choice Theory” Economics (language, theory) “Expected Utility” = calculation of all risks and rewards This is much broader than deterrence 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 ECEN2260 R. W. Erickson1.Bode plots: basic rulesA Bode plot is a plot of phase of a transfer function or otherdecibels, and phase in are plotted vs. frequency, using semi-logarithmic axes. The magni