Math Problem Statement

Which mapping represents y as a function of x?

Solution

To determine which mapping represents yy as a function of xx, we need to check each option to see if each input value (xx) is mapped to only one output value (yy). In mathematical terms, a function means that for every xx in the domain, there is exactly one yy in the codomain. Let's analyze each option:

  1. Option A:

    • Each xx value (0.25, 0.35, 0.45, 0.55) maps to a unique yy value (0.50, 0.70, 0.90, 1.10).
    • This satisfies the condition for a function because every xx has only one corresponding yy.
  2. Option B:

    • The xx values 20 and 40 both map to y=5y = 5.
    • The xx values 60 and 80 both map to y=15y = 15.
    • This does not satisfy the condition for a function, as multiple xx values are mapping to the same yy, indicating ambiguity in the xx-yy relationship.
  3. Option C:

    • Each xx value (−5, 0, 4) maps to a unique yy value (−5, −9, −13, −17).
    • This satisfies the condition for a function because every xx has only one corresponding yy.
  4. Option D:

    • The xx values −1.5, −1.0, −0.5, and 0.5 each map to two yy values (e.g., −1.5 maps to both 1.0 and 1.5).
    • This does not satisfy the condition for a function, as each xx value should correspond to only one yy value.

Conclusion

The correct answer is Option A, as it is the only mapping where each xx value has a unique yy value, thus representing yy as a function of xx.

Would you like more details on this explanation or have any questions?

Here are five additional related questions:

  1. What is the formal definition of a function in mathematics?
  2. Why does option D not satisfy the definition of a function?
  3. How can you visually determine if a mapping is a function?
  4. What is the significance of each input having only one output in functions?
  5. 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