Math Problem Statement
Solution
To determine which representation shows as a function of , we need to ensure that each -value is paired with exactly one -value. In mathematical terms, a function is defined such that for every input , there is only one output .
Here is the analysis of each option:
A
The -value is associated with three -values: , , and . This violates the definition of a function. Not a function.
B
The -values are each paired with exactly one -value. This is a function.
C
The -value is associated with two -values: and . This violates the definition of a function. Not a function.
D
The -value is associated with two -values: and . This violates the definition of a function. Not a function.
Final Answer:
The correct representation that shows as a function of is B.
Would you like further clarification or details?
Here are some follow-up questions to expand on this topic:
- What is the formal definition of a function in mathematics?
- How can you determine if a mapping diagram represents a function?
- Can a function have repeated -values for different -values?
- What are real-world examples of situations that can be modeled as functions?
- How do vertical line tests help in identifying functions in graphical representations?
Tip: Always check for unique outputs for each input to verify if a relation is a function.
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Mapping
Formulas
-
Theorems
Definition of a Function
Suitable Grade Level
Grades 6-8