#### Solved Examples and Worksheet for Determining a given Relation is a Function

Q1Draw the mapping diagram for the relation and determine whether it is a function or not.
{(2, 4), (- 8, 0), (1, 5), (3, 1)} A. Figure 3, Relation is a function
B. Figure 2, Relation is not a function
C. Figure 4, Relation is not a function
D. Figure 1, Relation is a function

Step: 1
Draw the mapping diagram for the given relation. Step: 2
A relation is a function if each element in the domain is paired with one and only one element in the range.
Step: 3
From the mapping diagram, it can be observed that the given relation is a function.
Correct Answer is :   Figure 1, Relation is a function
Q2Determine whether the relation is a function. Identify the domain and range, if it is a function.
 Input Output - 5 - 9 - 6 - 11 - 5 - 13 - 8 - 15

A. it is a function, domain: - 9, - 11, - 13 and - 15, range: - 5, - 6, - 7 and - 8
B. it is not a function
C. it is a function, domain: - 5, - 6, - 7 and - 8, range: - 9, - 11, - 13 and - 15
D. it is a function, domain: - 5, - 9, - 6 and - 11, range: - 7, - 13, and - 8

Step: 1
A relation is a function if every input has exactly one output.
Step: 2
The relation given is not a function because the input - 5 has two outputs - 9 and - 13.
Correct Answer is :   it is not a function
Q3Determine whether the relation represented by the set of ordered pairs below is a function. Give the domain and range, if it is a function.
(2, - 4), (2, 5), (2, - 6), (4, 7).

A. It is a function, domain: 2 and 4, range: 3, - 4, 5, - 6 and 7
B. It is not a function
C. It is a function, domain: 2, 5 and 7, range: - 4, 5, - 6 and 7
D. It is a function, domain: 2 and 4, range: - 4, 5, - 6 and 7

Step: 1
A relation is a function if every input has exactly one output.
Step: 2
The relation is not a function because the input 2 has three outputs: - 4, 5 and - 6.
Correct Answer is :   It is not a function
Q4Determine whether the relation is a function. Give the domain and range of it, if it is a function. A. it is a function; domain is 1, 3, 5 and range is 6, 2, 10
B. it is a function; domain is 6, 2, 10 and range is 1, 3, 5
C. it is a function; domain is 1 and range is 2
D. it is not a function

Step: 1
In the relation, for each input there is exactly one output.
Step: 2
The relation is a function.
Step: 3
The domain of the function is 1, 3, and 5.
Step: 4
The range of the function is 6, 2, and 10.
Correct Answer is :   it is a function; domain is 1, 3, 5 and range is 6, 2, 10
Q5Determine whether the relation represented by the set of ordered pairs below is a function or not.
(22, - 24), (22, - 25), (23, - 26), (24, - 27).

A. It is a function.
B. It is not a function.
C. It is a function with same domain and range.
D. cannot be determined

Step: 1
The relation is a function, if there is exactly one output for every input.
Step: 2
In the given relation 22 has two outputs - 24 and - 25.
Step: 3
So, the relation represented in the set of ordered pairs is not a function.
Correct Answer is :   It is not a function.
Q6A relation is observed between the number of days of preparation by a student for math, science, and statistics tests and the points he scored. The relation is: {(6, 64), (7, 94), (5, 54)}. Determine if this relation is a function or not.

A. It is a function.
B. It is not a function.
C. It is a function with same domain and range.
D. cannot be determined

Step: 1
The given ordered pairs are: {(6, 64), (7, 94), (5, 54)}
Step: 2
A relation is a function if each input corresponds to one and only one output.
Step: 3
So, the given relation is a function.
Correct Answer is :   It is a function.
Q7Determine whether the relation represented in the graph is a function or not. Find the domain and range, if it is a function. A. It is a function, domain: 1, 3, and 5; range: 2, 3, and 5.
B. It is a function, domain: 1, 2, 3, and 6; range: 2, 3, 4, and 6.
C. It is a function, domain: 2, 3, 4, 5, and 6; range: 1, 2, 3, 4, 5, and 6.
D. It is not a function.

Step: 1
A relation is a function if every input has exactly one output.
Step: 2
In the plot, for each x-coordinate, there is only one y-coordinate.
Step: 3
So, the relation is a function.
Step: 4
The domain is 1, 2, 3, and 6 and the range is 2, 3, 4, and 6.
Correct Answer is :   It is a function, domain: 1, 2, 3, and 6; range: 2, 3, 4, and 6.
Q8Determine whether the relation is a function or not. Find the range of it, if it is a function. A. It is not a function.
B. It is a function; range is 11, 13, 17, 19.
C. It is a function; range is 11.
D. It is a function; range is 2, 3, 5, 7.

Step: 1
A relation is a function if every input has exactly one output.
Step: 2
For each input 2, 3, 5, and 7, there is exactly one output.
Step: 3
So, the relation is a function.
Step: 4
Range is 11, 13, 17, and 19.
Correct Answer is :   It is a function; range is 11, 13, 17, 19.
Q9Determine whether the relation is a function or not. Give the domain and range of it, if it is a function. A. It is a function; domain is {6, 2, 10} and range is {1, 3, 5}.
B. It is a function; domain is {1, 3, 5} and range is {6, 2, 10}.
C. It is not a function.
D. It is a function; domain is {1} and range is {2}.

Step: 1
In the relation, for each input there is exactly one output.
Step: 2
The relation is a function.
Step: 3
The domain of the function is {1, 3, 5}.
Step: 4
The range of the function is {6, 2, 10}.
Correct Answer is :   It is a function; domain is {1, 3, 5} and range is {6, 2, 10}.
Q10Determine whether the relation is a function or not. Identify the domain and range, if it is a function.
 Input Output - 4 - 7 - 5 - 9 - 4 - 11 - 7 - 13

A. It is a function, domain: {- 7, - 9, - 11, - 13}, range: {- 4, - 5, - 6, - 7}.
B. It is not a function.
C. It is a function, domain: {- 4, - 7, - 5, - 9}, range: {- 6, - 11, - 7}.
D. It is a function, domain: {- 4, - 5, - 6, - 7}, range: {- 7, - 9, - 11, - 13}.

Step: 1
A relation is a function if every input has exactly one output.
Step: 2
The relation given is not a function because the input - 4 has two outputs - 7 and - 11.
Correct Answer is :   It is not a function.
Q11Determine whether the relation is a function or not. If so, find its domain and range.
{(2, - 1), (5, - 1), (- 7, - 1), (2, 3)}

A. It is a function, domain: {2, 7, - 5, 2}, range: {- 1, 3}.
B. It is a function, domain: {- 2, 5, - 7, 2}, range: {- 1, 3}.
C. It is not a function.
D. It is a function, domain: {- 1, 3}, range: {- 2, 5, - 7, 2}.

Step: 1
A relation is a function if for every input there is exactly one output.
Step: 2
The relation given is not a function because the input 2 has two outputs - 1 and 3.
Correct Answer is :   It is not a function.
Q12Determine whether the relation represented by the set of ordered pairs below is a function. Give the domain and range, if it is a function.
(5, - 7), (5, 8), (5, - 9), (7, 10).

A. It is a function, domain: 5, 8, and 10, range: - 7, 8, - 9 and 10
B. It is a function, domain: 5 and 7, range: - 7, 8, - 9 and 10
C. It is not a function
D. It is a function, domain: 5 and 7, range: 6, - 7, 8, - 9 and 10

Step: 1
A relation is a function if every input has exactly one output.
Step: 2
The relation is not a function because the input 5 has three outputs: - 7, 8, and - 9.
Correct Answer is :   It is not a function
Q13Draw the mapping diagram for the relation and determine whether it is a function or not.
{(2, 16), (4, 12), (6, 8), (8, 4)} A. Figure 2, Relation is not a function
B. Figure 1, Relation is a function
C. Figure 3, Relation is a function
D. Figure 4, Relation is not a function

Step: 1
Draw the mapping diagram for the given relation. Step: 2
A relation is a function if each element in the domain is paired with one and only one element in the range.
Step: 3
From the mapping diagram, it can be observed that the given relation is a function.
Correct Answer is :   Figure 1, Relation is a function
Q14Determine whether the relation is a function or not. Give the domain and range, if it is a function.
 Input Output 5 7 6 8 7 9 8 10

A. It is a function, domain: 7, 8, 9 and 10 range: 5, 6, 7 and 8
B. It is a function, domain: 5, 6, 7 and 8 range: 7, 8, 9 and 10
C. It is not a function
D. None of the above

Step: 1
For each input there is exactly one output.
Step: 2
So, the relation is a function.
Step: 3
The domain is 5, 6, 7 and 8. The range is 7, 8, 9 and 10.
Correct Answer is :   It is a function, domain: 5, 6, 7 and 8 range: 7, 8, 9 and 10
• Function