PPT-Asymptotes

Jacques Paradis Professeur Département de mathématiques 2 Plan de la rencontre Élément de compétence Définition dasymptote Asymptotes verticales Asymptotes horizontales Levée dindéterminations. In particular if the degree of is strictly less than that of d then the axis will be the horizontal asymptotea geometrical condition that can be expressed analytically by saying 0 as and as If the degree of is greater than or equal to the degree of Background There are three types of asymptotes horizontal vertical and oblique Type Equation De64257ning Property Horizontal lim lim Vertical lim lim lim lim Oblique ax lim ax 0 lim ax 0 The Asymptotes command generally returns all a Graphically. What is happening in the graph below?. Graphically. We can make the following statements:. ALSO:. Vertical Asymptotes. When do vertical asymptotes occur algebraically?. Denominator. = 0. Section 2.2b. End Behavior Models. For large values of . x. , we can sometimes model the behavior of. a. complicated function by a simpler one that acts in virtually the. s. ame way…. Ex: Given:. Show that while . By the end of today, you should be able to:. Graph the sine and cosine functions. Find the amplitude, period, and frequency of a function. Model Periodic behavior with sinusoids. Unit Circle. The Sine Function: y = . 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 . RevIEw. precalculus. y = (x+2). 2. y = (x-2). 2 . -1. y = -(x+1). 2 . + 3. 4) . The number of horsepower . H. required to overcome wind drag on a certain car is approximated by . H(s) = 0.002s. 2. + 0.05s - 0.029 , 0 < s < 100. Hyperbola: a set of all points (x, y) the difference of whose distances from two distinct fixed points (. foci. ) is a positive constant. . Similar to ellipse, which is the SUM of distances. Every hyperbola has two disconnected branches. The line through the foci intersects a hyperbola at its two . Definitions. . A. . hyperbola. . is the set of all point P such that the difference of the distances between P and two fixed points, called the . foci. , is a constant. . The. . transverse axis. . . 2. x. Domain:. Range:. Continuity:. Increasing/Decreasing:. Symmetry:. Boundedness:. Extrema:. Asymptotes:. End Behavior:. Domain:. Range:. Continuity:. Increasing/Decreasing:. Symmetry:. Boundedness:. By the end of today, you should be able to:. Graph the sine and cosine functions. Find the amplitude, period, and frequency of a function. Model Periodic behavior with sinusoids. Unit Circle. The Sine Function: y = . A brief journey into Section . 4.5a. Analysis of the Tangent Function. by. Domain: All . reals. except odd. multiples of. Range:. Continuous on its domain. Increasing on each interval in. i. ts domain. 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 . 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