To graph the rational function and show the x-andy-intercepts and asymptotes.
Explanation of Solution
Given information:
The rational function is
Graph:
Factor:
x-intercepts: the x-intercept are the zeros of the numerator,
So, x-intercept is
y-intercepts: to find y-intercept, substitute
So, y-intercept is
Horizontal asymptote: because here is degree of numerator same denominator so horizontal asymptote
Vertical asymptote: the vertical asymptote is occurs where denominator is zero, but here the denominator has imaginary roots so vertical asymptote does not occur.
Slant asymptote: the slant asymptote is occurs when the numerator degree is one more than denominator,
So vertical asymptote is
Use the above information together with some additional values which is show in table below
To sketch the graph,
x | y |
-2 | -0.55 |
-1 | -2.67 |
1 | -2.67 |
2 | -0.55 |
The graph is obtained as:
Interpretation:
From the above graph it can be observed that the x-intercept is
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning