Module 5  Limits and Infinity 
Introduction  Lesson 1  Lesson 2  Lesson 3  Lesson 4  SelfTest 
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 TI89 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
The graph of looks like the graph of the parabola y = x^{2} – 8x – 15 in this large viewing window. The Narrow View
The graph of looks like the graph of in this window. A Medium View To show both the vertical and parabolic asymptotic behavior of
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. 
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