Math Problem Statement

he list of ordered pairs below represents a function. { ( 6 , − 6 ) , ( − 3 , − 1 ) , ( 1 , − 8 ) , ( 5 , − 4 ) }

Solution

The list of ordered pairs you provided represents a function because:

  • A function is a relation where each input (or xx-value) is associated with exactly one output (or yy-value).
  • In your list, each xx-value is unique, which ensures that each input has a corresponding output.

Here’s the set you provided:

{(6,6),(3,1),(1,8),(5,4)}\{ (6, -6), (-3, -1), (1, -8), (5, -4) \}

Let's check the xx-values:

  • 66 maps to 6-6
  • 3-3 maps to 1-1
  • 11 maps to 8-8
  • 55 maps to 4-4

Since there are no repeated xx-values, this is indeed a function.

Would you like more details on how to identify whether a set of ordered pairs represents a function? Or do you have any specific questions about this example?


Related Questions:

  1. What is the difference between a function and a relation?
  2. Can a set of ordered pairs have multiple yy-values for one xx-value?
  3. How can you graph the function represented by a set of ordered pairs?
  4. How do you find the domain and range of a function from ordered pairs?
  5. What is a function’s inverse, and how do you find it from ordered pairs?

Tip: When checking if a set of ordered pairs represents a function, always look for unique xx-values. If any xx-value repeats with different yy-values, it is not a function!

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Math Problem Analysis

Mathematical Concepts

Functions
Ordered Pairs
Relations

Formulas

-

Theorems

Vertical Line Test
Definition of a Function

Suitable Grade Level

Grades 7-9