Concept explainers
(a)
The graph of the function applying the lead coefficient test.
(a)
Explanation of Solution
Given information:
The polynomial function as given below,
Formula used:
The horizontal axis represents the x- axis and the vertical axis represents the y-axis.
Calculation:
The leading coefficient test says that: 1- If the degree of the polynomial is even and the leading coefficient is positive, both ends of the graph rise up. 2. If the degree is even and the leading coefficient is negative, both ends of the graph fall down. 3- If the degree is odd and the leading coefficient is positive, the left side of the graph falls down and the right side rises up. 4. If the degree is odd and the leading coefficient is negative, the left side of the graph rises up and the right side falls down.
As the leading coefficient is negative and degree is odd, the graph rises up on the left side and falls down on the right.
The graph’s ends would be as shown below:
Conclusion:
The graph is plotted against the II and IV quadrant.
(b)
The real zeros of the polynomial.
(b)
Answer to Problem 78E
The value of x is
Explanation of Solution
Given information:
The polynomial function as given below,
Formula used:
The polynomial is equated to zero.
Calculation:
The leading coefficient test says that: 1- If the degree of the polynomial is even and the leading coefficient is positive, both ends of the graph rise up. 2. If the degree is even and the leading coefficient is negative, both ends of the graph fall down. 3- If the degree is odd and the leading coefficient is positive, the left side of the graph falls down and the right side rises up. 4. If the degree is odd and the leading coefficient is negative, the left side of the graph rises up and the right side falls down.
Putting
Adding these points to the graph, the graph would be as shown below,
Conclusion:
The value of x is
(c)
The plotting of sufficient solution points.
(c)
Answer to Problem 78E
The graphs get increases and decreases continuously.
Explanation of Solution
Given information:
The polynomial function as given below,
Formula used:
The horizontal axis represent the x-axis and the vertical axis represent the y-axis.
Calculation:
The leading coefficient test says that: 1- If the degree of the polynomial is even and the leading coefficient is positive, both ends of the graph rise up. 2. If the degree is even and the leading coefficient is negative, both ends of the graph fall down. 3- If the degree is odd and the leading coefficient is positive, the left side of the graph falls down and the right side rises up. 4. If the degree is odd and the leading coefficient is negative, the left side of the graph rises up and the right side falls down.
The polynomial function is evaluated at the values chosen between the test intervals. And the test interval is determined by the values of the zeros. Consider the table of values shown below:
Conclusion:
The graphs get increases and decreases continuously.
(d)
The continuous curve through the points.
(d)
Answer to Problem 78E
The graph cuts the x-axis at
Explanation of Solution
Given information:
The polynomial function as given below,
Formula used:
The zeros are of odd multiplicity
Calculation:
The leading coefficient test says that: 1- If the degree of the polynomial is even and the leading coefficient is positive, both ends of the graph rise up. 2. If the degree is even and the leading coefficient is negative, both ends of the graph fall down. 3- If the degree is odd and the leading coefficient is positive, the left side of the graph falls down and the right side rises up. 4. If the degree is odd and the leading coefficient is negative, the left side of the graph rises up and the right side falls down.
A continuous curve through the points obtained in the table is drawn. It is to be noted that as all the zeros are of odd multiplicity, the graph cuts the x-axis at
The graph is as shown below:
Conclusion:
The graph cuts the x-axis at
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- 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