(a)
The range and domain of a relation
(a)
Answer to Problem 1CT
Solution:
The domain of the relation is
The range of the relation is
The relation is a function.
Explanation of Solution
Given information:
The relation is
In the relation
That is, in a set of order pairs, first coordinate of each order pair is an element of domain.
Therefore, the domain is
Also, in a set of order pairs, second coordinate of each order pair is an element of range.
Therefore, the range is
As output is different for each input, the relation is a function.
(b)
The range and domain of a relation
(b)
Answer to Problem 1CT
Solution:
The domain of the relation is
The range of the relation is
The relation is not a function.
Explanation of Solution
Given information:
The relation is
In the relation
In a set of order pairs, first coordinate of each order pair is an element of domain.
Therefore, the domain is
In a set of order pairs, second coordinate of each order pair is an element of range.
Therefore, the range is
For input
Therefore, the relation
(c)
The range and domain of a relation and whether the relation is a function or not where the relation is
(c)
Answer to Problem 1CT
Solution:
The domain of the relation is
The range of the relation is
The relation is not a function.
Explanation of Solution
Given information:
The relation is:
Domain is set of
Therefore, from graph, domain of relation is
The relation have minimum value at
Thus, the range of relation is
From graph, for
Thus, the relation is not a function.
(d)
The range and domain of a relation and whether the relation is a function or not where the relation is
(d)
Answer to Problem 1CT
Solution:
The domain of the relation is
The range of the relation is
The relation is a function.
Explanation of Solution
Given information:
The relation is
Domain is set of
Therefore, from graph, domain of relation is
The relation have minimum value at
Thus, the range of relation is
From graph, for each
Thus, the relation is afunction.
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Precalculus (10th Edition)
Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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