Math Problem Statement
State whether each relation represents a function based on the mappings provided.
Solution
This image contains a set of mappings for six different relations. The task is to determine whether each relation represents a function. For a relation to be a function, each input (element in the left oval) must be mapped to exactly one output (element in the right oval). No input can have more than one arrow pointing to different outputs.
Analysis:
-
Relation 1:
- Each input maps to exactly one output.
- Conclusion: This is a function.
-
Relation 2:
- The input
-19
maps to two outputs:-16
and-13
. - Conclusion: This is not a function.
- The input
-
Relation 3:
- The input
-5
maps to both10
and14
. - Conclusion: This is not a function.
- The input
-
Relation 4:
- Each input maps to exactly one output.
- Conclusion: This is a function.
-
Relation 5:
- Each input maps to exactly one output.
- Conclusion: This is a function.
-
Relation 6:
- The input
0
maps to both1
and4
. - Conclusion: This is not a function.
- The input
Final Results:
- Function
- Not a function
- Not a function
- Function
- Function
- Not a function
Would you like me to explain why certain relations failed to qualify as functions in greater detail?
Related Questions:
- What are the defining characteristics of a function in mathematics?
- How can we represent functions using sets or tables?
- Can a function have duplicate outputs for different inputs?
- What are real-world examples of functions and non-functions?
- How are functions represented graphically, and what does the vertical line test indicate?
Tip: To confirm if a relation is a function, always check that each input has only one unique output!
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Math Problem Analysis
Mathematical Concepts
Relations and Functions
Mappings
Formulas
-
Theorems
Definition of a Function
Suitable Grade Level
Grades 8-10