|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
The graph of looks like the graph of the parabola y = x2 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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