Math Problem Statement
Solution
To determine which mapping represents as a function of , we need to check each option to see if each input value () is mapped to only one output value (). In mathematical terms, a function means that for every in the domain, there is exactly one in the codomain. Let's analyze each option:
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Option A:
- Each value (0.25, 0.35, 0.45, 0.55) maps to a unique value (0.50, 0.70, 0.90, 1.10).
- This satisfies the condition for a function because every has only one corresponding .
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Option B:
- The values 20 and 40 both map to .
- The values 60 and 80 both map to .
- This does not satisfy the condition for a function, as multiple values are mapping to the same , indicating ambiguity in the - relationship.
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Option C:
- Each value (−5, 0, 4) maps to a unique value (−5, −9, −13, −17).
- This satisfies the condition for a function because every has only one corresponding .
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Option D:
- The values −1.5, −1.0, −0.5, and 0.5 each map to two values (e.g., −1.5 maps to both 1.0 and 1.5).
- This does not satisfy the condition for a function, as each value should correspond to only one value.
Conclusion
The correct answer is Option A, as it is the only mapping where each value has a unique value, thus representing as a function of .
Would you like more details on this explanation or have any questions?
Here are five additional related questions:
- What is the formal definition of a function in mathematics?
- Why does option D not satisfy the definition of a function?
- How can you visually determine if a mapping is a function?
- What is the significance of each input having only one output in functions?
- How could you represent these mappings as ordered pairs?
Tip: When checking if a relation is a function, ensure that each input corresponds to only one output.
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Mapping Diagrams
Formulas
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Theorems
Definition of a Function
Suitable Grade Level
Grades 7-9