Math Problem Statement
Determine whether the relation defines a function, and give the domain and range. {(9, 3), (8, 7), (5, 1), (2, 4)}
Solution
To determine whether the given relation defines a function, we need to verify if each input (or first element) is associated with exactly one output (or second element). In other words, for every distinct -value, there should be a unique -value.
The relation is:
Step 1: Check if the relation is a function.
- In the ordered pairs, the first elements are , which are all distinct.
- Since each -value has exactly one corresponding -value, the relation does define a function.
Step 2: Determine the domain.
The domain is the set of all possible -values (first elements) in the relation:
Step 3: Determine the range.
The range is the set of all possible -values (second elements) in the relation:
Conclusion:
- The relation defines a function.
- Domain:
- Range:
Would you like further details or have any questions?
Here are 5 related questions to deepen understanding:
- What conditions must a relation meet to be considered a function?
- How do we determine the domain and range for more complex relations?
- Can a relation still be a function if two different -values map to the same -value?
- What are the differences between injective, surjective, and bijective functions?
- How would the answer change if one -value was associated with two different -values?
Tip: Always check the uniqueness of each -value's corresponding -value to confirm if 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 8-10