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Find the asymptotes of the graph of the rational function.
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Answer to Problem 89E
Explanation of Solution
Given: the rational function
Concept Used:
There are three kinds of asymptotes: horizontal, vertical and oblique.
An asymptote is a line that the graph of a function approaches but never actually touches. There are vertical asymptotes, horizontal asymptotes, and oblique asymptotes. Oblique asymptotes are also called slant asymptotes.
Vertical and horizontal asymptotes are vertical and horizontal lines, respectively. An oblique, or slant, asymptote is an asymptote that is neither vertical nor horizontal | ![]() |
Calculation:
To find the vertical asymptotes, simply make denominator equal to zero and solve for x.
For Horizontal Asymptotes, if the degree os the numerator is equal to the degree of the denominator, in this case the asymptote is the horizontal line
Vertical Asymptote: Denominator = 0
Horizontal Asymptotes: For ; the leading coefficient in Numerator a = 2 and the leading coefficient in Denominator b = 1 Horizontal Asymptote is the horizontal line Vertical Asymptote: Horizontal Asymptote: | ![]() |
Thus, Vertical Asymptote:
Chapter 4 Solutions
Precalculus with Limits: A Graphing Approach
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