The correct definition for the term “relation” from the options;
A.A set of ordered pairs.
B.The ratio of change in y to the change in x along a line.
C.The set of all possible values of the independent variable.
D.All the second components of a set of ordered pairs.
Answer to Problem 1TYWP
Solution:
The correct definition for the term “relation”, is option (A) and the definition is “a set of ordered pairs”.
Explanation of Solution
Given Information:
The options are,
A. A set of ordered pairs.
B. The ratio of change in y to the change in x along a line.
C. The set of all possible values of the independent variable.
D. All the second components of a set of ordered pairs.
Consider the option (A).
A.A set of ordered pairs:
A relation represents a relationship between sets of values. Hence it is represented as a set of ordered pairs.
For example, the set of ordered pairs like
So, this option (A) is correct.
Consider the option (B).
B.The ratio of change in y to the change in x along a line:
The ratio of change in y to the change in x along a line is called the slope of a line. Hence it cannot represent a relation.
So, this option (B) is incorrect.
Consider the option (C).
C.The set of all possible values of the independent variable:
The set of all possible values of the independent variable x is called the domain. So, these values represent the first component of the ordered pairs, but the not ordered pair. Hence, the set of all possible values of the independent variable cannot represent a relation.
So, this option (C) is incorrect.
Consider the option (D).
D.All the second components of a set of ordered pairs:
All the second components of a set of ordered pairs are the possible values of the dependent variable y or the range of the relation. So, it cannot represent a relation.
So, this option (D) is incorrect.
Hence, the correct definition is “a set of ordered pairs” that is option (A).
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Chapter 9 Solutions
Beginning and Intermediate Algebra (6th Edition)
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