Math Problem Statement

Which set of ordered pairs represents a function?

Solution

To determine which set of ordered pairs represents a function, we need to ensure that each input (or "x" value) is associated with only one output (or "y" value). In other words, no x-value should repeat with different y-values.

Let’s analyze each option:

  1. Set 1: {(3,8),(6,1),(6,9),(0,1)}\{(-3, 8), (-6, -1), (-6, -9), (0, 1)\}

    • The x-value 6-6 is paired with two different y-values: 1-1 and 9-9.
    • This set does not represent a function.
  2. Set 2: {(9,8),(4,1),(4,4),(0,6)}\{(-9, -8), (4, 1), (4, -4), (0, -6)\}

    • The x-value 44 is paired with two different y-values: 11 and 4-4.
    • This set does not represent a function.
  3. Set 3: {(1,2),(4,2),(0,3),(0,8)}\{(1, 2), (-4, -2), (0, 3), (0, -8)\}

    • The x-value 00 is paired with two different y-values: 33 and 8-8.
    • This set does not represent a function.
  4. Set 4: {(2,5),(6,5),(1,7),(7,1)}\{(2, -5), (6, -5), (-1, 7), (7, -1)\}

    • Each x-value is unique and has only one corresponding y-value.
    • This set does represent a function.

Answer: The correct answer is Set 4: {(2,5),(6,5),(1,7),(7,1)}\{(2, -5), (6, -5), (-1, 7), (7, -1)\}.

Would you like a detailed explanation on why a function requires unique x-values?

Here are some related questions to practice:

  1. How can you identify a function from a graph?
  2. What is the "vertical line test" for functions?
  3. What happens when multiple x-values share the same y-value? Is it still a function?
  4. How can functions be represented using tables, mappings, or graphs?
  5. What is the difference between one-to-one functions and regular functions?

Tip: Remember, in a function, each input (x) must be associated with exactly one output (y).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Functions
Ordered Pairs

Formulas

-

Theorems

Definition of a Function

Suitable Grade Level

Grades 8-10