Concept explainers
Describe the right-hand and left-hand behavior of the graph of the polynomial function
Answer to Problem 26RE
The graph falls to the left and rises to the right.
Explanation of Solution
Given information:
Concept used:
Let
According to leading coefficient test, there are 4 cases;
Cases | Behavior of graph |
When n is odd and | Graph falls to the left and rises to the right |
When n is odd and | Graph rises to the left and falls to the right |
WhWhen n is odd and | Graph rises to the left and right |
WhWhen n is odd and | Graph falls to the left and right |
Calculation for graph:
Consider
x | f ( x ) |
-2 | -159 |
-1 | -2 |
0 | 5 |
1 | 6 |
2 | 97 |
By taking different values of x , the graph can be plotted.
Graph:
Interpretation:
The degree of given function is 5, which is odd.
The leading coefficient of given function is 4, which is positive.
So, according to leading coefficient test, the graph falls to the left and rises to the right.
Chapter 2 Solutions
Precalculus with Limits: A Graphing Approach
- 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