Math Problem Statement
Solution
The diagram shows a relation between two sets, where the left set contains the elements {13, 17, 5}, and the right set contains {11, 14}. We need to determine whether this relation defines a function and also provide the domain and range.
1. Is this relation a function?
To qualify as a function, each element of the domain (the set on the left) must map to exactly one element in the range (the set on the right). Upon reviewing the arrows:
- 13 maps to 11.
- 17 maps to 11.
- 5 maps to 14.
Each element of the domain maps to exactly one element in the range. Therefore, this is a function.
2. Domain and Range
- The domain is the set of all inputs (the elements from the first set): {13, 17, 5}.
- The range is the set of all outputs (the elements from the second set that are mapped by at least one input): {11, 14}.
Answer Explanation:
- The relation defines a function since each element of the domain maps to one element in the range.
- The domain is {13, 17, 5}.
- The range is {11, 14}.
Correct multiple-choice answers:
- The correct answer to whether this is a function is A: "Yes, because each element of the domain (first component) is distinct and corresponds to exactly one range element (second component)."
- For the domain, you should select the answer where the domain is the set {13, 17, 5}.
Do you want further explanation on any part?
5 Follow-Up Questions:
- What makes a relation not a function?
- How is the range determined in a function?
- Can a function map multiple domain elements to the same range element?
- How do you find the domain and range in more complex functions, like those involving variables?
- What are some examples of relations that are not functions?
Tip:
Always check if any domain element maps to more than one range element when determining whether a relation is a function!
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Domain and Range
Formulas
-
Theorems
Definition of a function
Suitable Grade Level
Grades 6-8
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