Module 5 - Limits and Infinity Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Lesson 4 | Self-Test Lesson 5.4: Nonlinear Asymptotes In this lesson you will examine a rational fraction with a nonlinear asymptote. Using propFrac( will be helpful in determining the equation of the nonlinear asymptote. 5.4.1 Use your TI-89 to rewrite the rational function as a polynomial plus a proper fraction. Click here for the answer. 5.4.2 What do the parts of the proper fraction tell you about the graph of ? Click here for the answer. Provide graphical support for the answer to Question 5.4.2 by graphing the function in a large window and in a window near x = 2. The Wide View Enter into y1 and y = x2 – 8x – 15 into y2. Set the Window values to [-50, 50] x [-2500, 2500] with xscl = 10 and yscl = 500.  The graph of looks like the graph of the parabola y = x2 – 8x – 15 in this large viewing window. The Narrow View Replace y2 with the function Set the Window values to [0, 4] x [-500, 500] with xscl = 1 and yscl = 50 The graph of looks like the graph of in this window. A Medium View To show both the vertical and parabolic asymptotic behavior of Delete y2 in the Y= Editor Graph with line style Graph y2 = x2 – 8x – 15 with dot style. First enter y2 = x^2 - 8x - 15. Then place the cursor anywhere in y2 and press  . Finally press . Set the Window values to [-10, 15] x [-100, 150], xscl = 1, yscl = 50 As you have seen, the choice of viewing window can dramatically affect the appearance of a function, and different windows should be used to illustrate different features. The best graph is one in which all significant features of a function are displayed or implied. Such a graph is called a complete graph. Two or more windows are often needed to illustrate a complete graph. < Back | Next > ©Copyright 2007 All rights reserved. | Trademarks | Privacy Policy | Link Policy