Math Problem Statement

Which relation is a function?

Solution

The image contains four tables representing relations. To determine which one is a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). A relation is a function if each input value has only one output.

Let's analyze each table:

  1. First Table:

    • Input values: -6, -2, 0, 5
    • Each input corresponds to a unique output (-4, 1, 2, 3). This is a function.
  2. Second Table:

    • Input values: -3, 0, 3
    • Each input corresponds to a unique output (-2, -6, 1). This is a function.
  3. Third Table:

    • Input values: -2, -4, -2, 4
    • The input -2 is paired with two different outputs (1 and -1). This is not a function.
  4. Fourth Table:

    • Input values: -7, -7, 0, 2
    • The input -7 is paired with two different outputs (-1 and 4). This is not a function.

Based on this analysis, the first and second tables represent functions.

Would you like further clarification or have additional questions? Here are 5 follow-up questions you might find helpful:

  1. How do you test if a relation is a function?
  2. Can a function have more than one output for the same input?
  3. What is the difference between a function and a non-function?
  4. How do you graph a function from a table?
  5. Can a function have duplicate output values for different inputs?

Tip: A quick way to check if a table represents a function is to look for repeated x-values paired with different y-values. If this occurs, it's not a function.

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Math Problem Analysis

Mathematical Concepts

Relations and Functions
Input and Output Pairs

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8