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In the ordered set of pairs {(−3, 4), (5, −6), (−2, 7), (5, 3), (6, −8)} the domain and range will form:
- a)Value
- b)No Relations
- c)Function
- d)Not a function
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In the ordered set of pairs {(−3, 4), (5, −6), (−2, 7), (5, 3), (6, −...
The domain is {−3, −2, 5, 6} and range = {−8, −6, 3, 4, 7}.
Here we can see, for x = 5, there are two corresponding y values −6 and 3. So, this relation is not a function.
Also, there are four elements in the domain and five elements in the range. This implies two values in the range is associated with one value in the domain.
So, the given domain and range will not form a function.
Hence, the correct option is (D).
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Community Answer
In the ordered set of pairs {(−3, 4), (5, −6), (−2, 7), (5, 3), (6, −...
Understanding the Ordered Set of Pairs
In the given set of pairs: {(−3, 4), (5, −6), (−2, 7), (5, 3), (6, −8)}, we need to analyze whether it can be classified as a function.
Definition of a Function
A function is defined as a relation where each input (or domain value) is associated with exactly one output (or range value). This means that no two pairs can have the same first element (x-value) with different second elements (y-values).
Analyzing the Domain
- The domain consists of all the first elements (x-values) in the pairs:
- -3
- 5
- -2
- 5 (again)
- 6
- The unique x-values in the domain are: {-3, 5, -2, 6}.
Identifying Duplicates
- The x-value '5' appears twice in the pairs:
- (5, -6)
- (5, 3)
Conclusion on Functionality
- Since the x-value '5' is associated with two different y-values (-6 and 3), it violates the definition of a function.
- Thus, the relation cannot be classified as a function.
Final Answer
Based on this analysis, the correct option is 'D' - Not a function.
In the given set of pairs: {(−3, 4), (5, −6), (−2, 7), (5, 3), (6, −8)}, we need to analyze whether it can be classified as a function.
Definition of a Function
A function is defined as a relation where each input (or domain value) is associated with exactly one output (or range value). This means that no two pairs can have the same first element (x-value) with different second elements (y-values).
Analyzing the Domain
- The domain consists of all the first elements (x-values) in the pairs:
- -3
- 5
- -2
- 5 (again)
- 6
- The unique x-values in the domain are: {-3, 5, -2, 6}.
Identifying Duplicates
- The x-value '5' appears twice in the pairs:
- (5, -6)
- (5, 3)
Conclusion on Functionality
- Since the x-value '5' is associated with two different y-values (-6 and 3), it violates the definition of a function.
- Thus, the relation cannot be classified as a function.
Final Answer
Based on this analysis, the correct option is 'D' - Not a function.
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In the ordered set of pairs {(−3, 4), (5, −6), (−2, 7), (5, 3), (6, −8)} the domain and range will form:a)Valueb)No Relationsc)Functiond)Not a functionCorrect answer is option 'D'. Can you explain this answer?
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