Math Problem Statement

Which representation shows y as a function of x?

Solution

To determine which representation shows yy as a function of xx, we need to ensure that each xx-value is paired with exactly one yy-value. In mathematical terms, a function is defined such that for every input xx, there is only one output yy.

Here is the analysis of each option:

A

The xx-value 22 is associated with three yy-values: 1414, 99, and 11. This violates the definition of a function. Not a function.

B

The xx-values 2,1,0,4-2, -1, 0, 4 are each paired with exactly one yy-value. This is a function.

C

The xx-value 1-1 is associated with two yy-values: 5-5 and 33. This violates the definition of a function. Not a function.

D

The xx-value 55 is associated with two yy-values: 7-7 and 77. This violates the definition of a function. Not a function.

Final Answer:

The correct representation that shows yy as a function of xx is B.

Would you like further clarification or details?

Here are some follow-up questions to expand on this topic:

  1. What is the formal definition of a function in mathematics?
  2. How can you determine if a mapping diagram represents a function?
  3. Can a function have repeated yy-values for different xx-values?
  4. What are real-world examples of situations that can be modeled as functions?
  5. 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