The relation for the mapping numbers onto letters and the mapping letters onto numbers and determine if the relations are functions.
Answer to Problem 2PS
The relation for the mapping number onto the letter is not a function as domain maps to multiple values in the range. The relation for the mapping letters on to the function is a relation as no two values in the range share a common domain.
Explanation of Solution
Consider the number
The case when the numbers are mapped onto the letters, the number are the part of the domain and the letters are the range. Since, on the telephone keypad the numbers probably maps to more than one letter, a single value on the domain can map to multiple values in the range that is it is not a function but a relation.
Thus, the relation is not a function as the number is more than the corresponding letter.
If the letters are mapped on the numbers than the letters are the part of the domain and the numbers are the part of the range. As in an ordinary telephone keypad the numbers have small letters, the values in the range than share a common value in the domain which is a domain. As every function is a relation than this is also a relation.
Thus, the function is the relation.
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