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,
y-intercepts: to find y-intercept, substitute
So, y-intercept is
Horizontal asymptote: because here is degree of numerator is greater than denominator so horizontal asymptote is none.
Vertical asymptote: the vertical asymptote is occurs where denominator is zero,
So vertical asymptote is
Slant asymptote: since the degree of the numerator is one more than the degree of the denominator, the function has a slant asymptote.
So slant asymptote is
Use the above information together with some additional values which is show in table below
To sketch the graph,
x | y |
-2 | -2.16 |
-1 | -0.20 |
1 | 3.66 |
2 | -5.5 |
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
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning