Math Problem Statement
Determine whether the relation is a function. Give the domain and the range of the relation. {(5,4),(5,7),(7,4),(7,7)} Question content area bottom Part 1 Is this a function?
Solution
A relation is considered a function if each input (the first element in each ordered pair) is associated with exactly one output (the second element in the pair).
Given the relation: we can observe that:
- The input 5 is associated with both 4 and 7.
- The input 7 is also associated with both 4 and 7.
Since the input 5 corresponds to two different outputs (4 and 7), this relation is not a function.
Domain and Range:
- Domain: The set of all inputs (first elements):
- Range: The set of all outputs (second elements):
Summary:
- Is it a function? No.
- Domain:
- Range:
Would you like further clarification or details on this concept?
Here are five related questions to expand on this information:
- What are the key differences between a function and a relation?
- How can you graphically determine if a relation is a function?
- Can a function have the same output for different inputs?
- What is the vertical line test for functions?
- What are some examples of real-world functions?
Tip: When checking if a relation is a function, remember that each input must map to exactly one output!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Relations and Functions
Domain and Range
Formulas
-
Theorems
Definition of Function
Vertical Line Test
Suitable Grade Level
Grades 9-11
Related Recommendation
Determine if the Relation {(3,1), (3,2), (7,1), (7,2)} is a Function
Determine If a Relation Is a Function and Find Its Domain and Range
Determine if a Relation is a Function: {(1, 2), (3, 4), (1, 5)}
Determine If a Relation is a Function with Domain and Range
Determine if a Relation is a Function and Find its Domain and Range