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Find the domain and range of the given relation. Determine if the relation defines y as a function of x. {(23, 4), (–16, –9), (–1, 7), (8, 20)}

Find the domain and range of the given relation. Determine if the relation defines y as a function of x. {(23, 4), (–16, –9), (–1, 7), (8, 20)}

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem: Domain and Range of a Relation** Find the domain and range of the given relation. Determine if the relation defines \( y \) as a function of \( x \). Given Relation: \[ \{(23, 4), (-16, -9), (-1, 7), (8, 20)\} \] **Solution:** - **Domain:** The set of all first elements in the ordered pairs. - Domain = \{23, -16, -1, 8\} - **Range:** The set of all second elements in the ordered pairs. - Range = \{4, -9, 7, 20\} - **Function Verification:** A relation defines \( y \) as a function of \( x \) if each element in the domain is associated with exactly one element in the range. - Since each \( x \) value in the domain corresponds to exactly one \( y \) value, the relation does define \( y \) as a function of \( x \).
Transcribed Image Text:**Problem: Domain and Range of a Relation** Find the domain and range of the given relation. Determine if the relation defines \( y \) as a function of \( x \). Given Relation: \[ \{(23, 4), (-16, -9), (-1, 7), (8, 20)\} \] **Solution:** - **Domain:** The set of all first elements in the ordered pairs. - Domain = \{23, -16, -1, 8\} - **Range:** The set of all second elements in the ordered pairs. - Range = \{4, -9, 7, 20\} - **Function Verification:** A relation defines \( y \) as a function of \( x \) if each element in the domain is associated with exactly one element in the range. - Since each \( x \) value in the domain corresponds to exactly one \( y \) value, the relation does define \( y \) as a function of \( x \).
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