Problem 109
Question
What is a relation? Describe what is meant by its domain and its range.
Step-by-Step Solution
Verified Answer
A relation is a set of ordered pairs, where every first element belongs to the domain and every second element belongs to the range. The domain is the set of all possible first elements (inputs, or x-values), while the range is the set of all possible second elements (outputs, or y-values).
1Step 1: Defining a Relation
A relation in mathematics is a set of ordered pairs (x, y), which describes a relationship between two elements, where x belongs to the first set (called the domain), and y belongs to the second set (called the range). In simpler terms, it's anything that links one set of values with another set of values.
2Step 2: Defining the Domain of a Relation
The domain of a relation is the set of all possible values that the first element (x) of the ordered pairs can take. It consists of all inputs, or x-values, which will 'produce' some output in the relation.
3Step 3: Defining the Range of a Relation
The range of a relation is the set of all possible values that the second element (y) of the ordered pairs can take. It refers to the output, or y-values, which can be 'produced' given the specific domain.
Other exercises in this chapter
Problem 108
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