Concept explainers
(a)
To write: The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units upward.
(a)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph is vertically (upward) shifted, add 2 to the
Thus, the equation of the graph of f becomes
(b)
To write: The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units downward.
(b)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph is vertically (upward) shifted, subtract 2 from the
Thus, the equation of the graph of f becomes
(c)
To write: The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units to the right side.
(c)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph is horizontally (right side) shifted, subtract 2 from x.
Thus, the equation of the graph of f becomes
(d)
To write: The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units to the left side.
(d)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph is horizontally (left side) shifted, add 2 to x.
Thus, the equation of the graph of f becomes
(e)
To write: The equation of the graph which is obtained from the given graph such that the graph reflects about the x axis.
(e)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph is reflecting about the x-axis, the obtained graph must be an odd function.
Therefore, substitute
Thus, the equation of the graph of f becomes
(f)
To write: The equation of the graph which is obtained from the given graph such that the graph reflects about the y axis.
(f)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph reflects about the x-axis, the obtained graph must be an even function.
Therefore, substitute
Thus, the equation of the graph of f becomes
(g)
To write: The equation of the graph which is obtained from the given graph such that the graph stretched vertically by a factor of 2.
(g)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph is stretched vertically by a factor of 2, multiply 2 to the
Thus, the equation of the graph of f becomes
(h)
To write: The equation of the graph which is obtained from the given graph such that the graph shrunk vertically by a factor of 2.
(h)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph is shrunk vertically by a factor of 2, divide 2 to the
Thus, the equation of the graph of f becomes
(i)
To write: The equation of the graph which is obtained from the given graph such that the graph stretched horizontally by a factor of 2.
(i)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph is stretched horizontally by a factor of 2, divide x by 2.
Thus, the equation of the graph of f becomes
(j)
To write: The equation of the graph which is obtained from the given graph such that the graph shrunk horizontally by a factor of 2.
(j)
Answer to Problem 11RCC
Solution:
The equation of the graph of f becomes
Explanation of Solution
Let the equation of the graph be
Since the graph is shrunk horizontally by a factor of 2, multiply
Thus, the equation of the graph of f becomes
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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