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,
here x-intercept does not exist.
y-intercepts: to find y-intercept, substitute
So, y-intercept is
Horizontal asymptote: here the degree of numerator is less than degree of denominator,
So horizontal asymptote is
Vertical asymptote: the vertical asymptote is occurs where denominator is zero,
So, the vertical asymptote is
Slant asymptote: : the slant asymptote is occurs when the numerator degree is one more than denominator, here the degree of denominator is greater than degree od numerator, so slant asymptote does not exist.
Use the above information together with some additional values which is show in table below
To sketch the graph,
x | y |
-3 | 1 |
-1 | 1 |
1 | .11 |
2 | 0.625 |
The graph is obtained as:
Interpretation:
From the above graph it can be observed that the x-intercept does not exist, y-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