To create: A function from the given graph by using transformations.
Answer to Problem 7E
The function of the shown graph is
Explanation of Solution
The equation of the given graph is
Let
Notice that the given graph is a semi-circle with the domain [0, 3] and the range [0, 1.5].
Also, it is observed from the given graph that the graph is shifted 4 units to the left and shifted 1 unit downward.
Moreover, the graph is reflected about the origin.
Thus, add 4 to x as it shifted 4 units to the left; subtract 1fromf(x)as it shifted 1 unit downward and then multiply f(x) by −1 as the graph reflects about x-axis.
Therefore, the given function will change as
Thus, the function of the shown graph is
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