Whether the function which reflects a person’s height at age t is one-to-one.
Answer to Problem 14E
The function is not a one-to one function.
Explanation of Solution
Result used:
Horizontal line test states that the graph of the function is one-to-one function if and only if a horizontal line intersects the graph exactly once.
Calculation:
The given function is,
It is known that the height of a person will remain constant after a certain age. That is the growth will be stopped and maintains a constant height for many years.
The graph of the function
From Figure 1, it is observed that the horizontal line intersects the curve at many points, which means it fails the horizontal line test.
Thus, it can be concluded that the function
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