(a)
Find the parent function
(a)
Answer to Problem 40E
For the function
Explanation of Solution
Parent function is the basic function of a family of functions that preserves the definitions, shape of its graph and properties of the entire family.
Parent function used in this question is the absolute value function i.e
To identify the parent function, strip all the arithmetic operations on the function to leave behind one higher order operation in just x.
To identify the parent function, strip all the arithmetic operations on the function to leave behind one higher order operation in just x.
Conclusion:
So, remove the arithmetic operation of subtraction of 2 from 2 and multiplication by 1/2 and then subtraction of 3 from the given funcion to get the parent function.
(b)
Find the sequence of transformation from f to g.
(b)
Answer to Problem 40E
The shape of
Explanation of Solution
Given information:
Concept Used:
The sequence of transformations from ƒ to g depicts the steps followed and the transformations used to reach from the parent function ƒ to g.
The sequence of transformations from
Types of shifts used in function transfromation:
1. Vertical shift: If
If
2. Horizontal Shift:If
If
3. Reflection:The graph for the function say
The graph for the function say
4. Vertical Stretching and Shrinking:If
If
5. Horizontal Stretching and Shrinking:If
If
Conclusion:
The sequence of transformations from ƒ to g depicts the steps followed and the transformations used to reach from the parent function ƒ to g.
The shape of drawn reflected in the x-axis and stretched by by 1/2 units and then shifted downward by 3 units is the required sequence of transformations from ƒ to g.
(c)
To sketch the graph of
(c)
Answer to Problem 40E
Explanation of Solution
Given information:
Use parent functionsand then move them around the coordinate plane through various types of shifts and thus write one function in terms of the other.
Conclusion:
Obtain the graph of
(d)
To write
(d)
Answer to Problem 40E
Explanation of Solution
Given information:
Multiply
Chapter 1 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