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.


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