In Exercises 1-6, determine whether each relation is a function. Give the domain and range for each relation.
1. {(2, 6), (1, 4), (2, −6)}
To find: The domain and range of the relation; also check whether the relation is a function or not.
Answer to Problem 1MC
The domain and range of the relation is
Explanation of Solution
Given:
The relation is
Definition used:
Relation:
“A relation is any set of ordered pairs and the set of all first component of the ordered pairs is called domain and the set of all second component of the relation is called the range of the relation.”
Function:
“A function is relation such that each element in the domain corresponds to exactly one element in the range”.
Interpretation:
Consider the relation,
Clearly, the first component of the above ordered pairs are
By the definition of the relation, the domain of the relation is the first components of the set of ordered pairs.
That is, the domain of the function is
Also, the second component of the ordered pairs are
By the definition of the relation, the range of the relation is the second component of the set of ordered pairs.
That is, the range of the function is
Draw a circle for the domain and range that will represent the above relation as shown in the below Figure 1.
From Figure 1, the element 2 is mapped into the elements 6 and
Also, the element 1 is mapped into 4.
That is, the set of ordered pairs
Since the element 2 is mapped into two elements in the range.
By the definition of the function, the relation is not a function.
Thus, the relation
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