
For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function.
1.
x | y | x | y |
-3 | 9 | 1 | 1 |
2 | 4 | 2 | 4 |
-1 | 1 | 3 | 9 |
0 | 0 |
a.

The domain and the range of given relation
Answer to Problem 1E
The domain is D∈{−3,−2,−1,0,1,2,3} and the range is R∈{0,1,4,9}
Explanation of Solution
Given:
We are given with a Table as below:
Concept Used:
A relation is defined as the set of ordered pairs. A function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output.
Here the set of input is known as Domain whereas the set of output is known as the Range.
Calculation:
Using the concept that a relation is defined as the set of ordered pairs and a function consists of three important parts, the input values, the output values and a rule or a set of rules which defines the relation between input and output. Here the set of input is known as Domain whereas the set of output is known as the Range.
So we can say the Domain is D∈{−3,−2,−1,0,1,2,3}
The range of the relation is R∈{0,1,4,9}
Conclusion:
The domain and the range of given relation is D∈{−3,−2,−1,0,1,2,3} and R∈{0,1,4,9} respectively.
b.

State whether the relation is a function.
Answer to Problem 1E
The given relation is a function.
Explanation of Solution
Given:
We are given with a Table as below:
Concept Used:
A function relates every elements of domain to exactly one element in the range.
Calculation:
Using the concept-A function relates every elements of domain to exactly one element in the range.
We can observe from the given table that every elements of domain relates to exactly one element in the range.
Hence the given relation is a function.
Conclusion:
The given relation is a function.
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Chapter 1 Solutions
Calculus Volume 1
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