To discuss: the given rational function
Answer to Problem 33RE
Explanation of Solution
Given:
Calculation:
STEP 1: The numerator and the denominator of
The domain of
Since 0 is in the domain, find the
Substitute 0 for
Therefore, the
STEP 2: The function
Determine the behaviour of the graph near the
Plot the point (-2,0) and indicate a line with slope -1 on the graph.
STEP 3: G is in lowest terms. The real zeros of the denominator are the real solutions of theequation
Graph the asymptote
STEP 4: Degree of the numerator is equal to the degree of the denominator. So, the graph has a horizontal asymptote. The leading coefficient of the numerator is 1 and that of the denominator is also 1 . Therefore, the graph of
Indicate this line on the graph using a dashed line.
Substitute
Multiply both the sides by
Subtract
There is no solution for
STEP 5: The zeros of the numerator and the denominator. - 1. - 2, and 2. Divide the x-axis into four intervals. The four intervals are
Now, construct the table.
Plot the points from the table obtained.
STEP6: Next, the behaviour of the graph near the asymptotes is to be determined.
The graph lies above the x -axis for x<-2 and y=1, is a horizontal asymptote. So, the graph is drawn at the top of the x -axis just approaching the asymptote $y=1$ at the bottom. Also note thatthe graph intersects the x-axis at the point (-2,0) .
The graph is drawn below the
The graph is drawn above the
The graph lies above the
STEP7: The figure shows the final graph.
Conclusion:
Thus, the given relation is discussed
Chapter 4 Solutions
Precalculus
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus (10th Edition)
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (3rd 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