Math Problem Statement
Solution
Let's solve the problem step-by-step.
We have the relation defined by the following set of ordered pairs:
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Domain of the Relation:
The domain is the set of all the first elements (x-values) of the ordered pairs.From the given pairs:
- The x-values are:
Since we only list each value once, the domain is:
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Range of the Relation:
The range is the set of all the second elements (y-values) of the ordered pairs.From the given pairs:
- The y-values are:
After removing duplicates, the range is:
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Is the Relation a Function?
To determine if the relation is a function, each input (x-value) must map to exactly one output (y-value). If an x-value maps to more than one y-value, it is not a function.In this relation:
- The x-value maps to both and .
Since has two different outputs, this means the relation is not a function.
Summary:
- Domain:
- Range:
- Is it a Function?: No, it is not a function.
Would you like more details on any part of the solution? Here are some related questions you might find interesting:
- What is the difference between a relation and a function?
- How do you determine the domain and range from a graph?
- Can a function have repeated y-values?
- What makes a relation a one-to-one function?
- How can you represent a function using a table?
Tip: Always remember that for a relation to be a function, each input must have exactly one output—this is the key defining property of functions.
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Math Problem Analysis
Mathematical Concepts
Relations
Functions
Domain
Range
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9