Math Problem Statement

Which set of ordered pairs represents a function?

Answer

Multiple Choice Answers

left curly bracket, left parenthesis, minus, 4, comma, minus, 6, right parenthesis, comma, left parenthesis, minus, 4, comma, minus, 8, right parenthesis, comma, left parenthesis, 0, comma, minus, 3, right parenthesis, comma, left parenthesis, 7, comma, 3, right parenthesis, right curly bracket{(−4,−6),(−4,−8),(0,−3),(7,3)}

left curly bracket, left parenthesis, minus, 2, comma, 1, right parenthesis, comma, left parenthesis, minus, 3, comma, 9, right parenthesis, comma, left parenthesis, minus, 3, comma, minus, 6, right parenthesis, comma, left parenthesis, 8, comma, minus, 4, right parenthesis, right curly bracket{(−2,1),(−3,9),(−3,−6),(8,−4)}

left curly bracket, left parenthesis, 8, comma, minus, 8, right parenthesis, comma, left parenthesis, 9, comma, 2, right parenthesis, comma, left parenthesis, minus, 8, comma, minus, 4, right parenthesis, comma, left parenthesis, 9, comma, minus, 9, right parenthesis, right curly bracket{(8,−8),(9,2),(−8,−4),(9,−9)}

left curly bracket, left parenthesis, minus, 9, comma, 0, right parenthesis, comma, left parenthesis, 0, comma, 0, right parenthesis, comma, left parenthesis, minus, 5, comma, minus, 2, right parenthesis, comma, left parenthesis, 9, comma, 2, right parenthesis, right curly bracket{(−9,0),(0,0),(−5,−2),(9,2)}

Solution

A set of ordered pairs represents a function if each input (first element in the pair) corresponds to exactly one output (second element in the pair). In other words, no two pairs should have the same first element with different second elements.

Let's examine each option:

  1. {(−4,−6),(−4,−8),(0,−3),(7,3)}\{(-4, -6), (-4, -8), (0, -3), (7, 3)\}

    • Here, the input −4-4 is associated with both −6-6 and −8-8, which means this set is not a function.

  2. {(−2,1),(−3,9),(−3,−6),(8,−4)}\{(-2, 1), (-3, 9), (-3, -6), (8, -4)\}

    • The input −3-3 is associated with both 99 and −6-6, so this set is not a function.

  3. {(8,−8),(9,2),(−8,−4),(9,−9)}\{(8, -8), (9, 2), (-8, -4), (9, -9)\}

    • The input 99 is associated with both 22 and −9-9, so this set is not a function.

  4. {(−9,0),(0,0),(−5,−2),(9,2)}\{(-9, 0), (0, 0), (-5, -2), (9, 2)\}

    • Each input is unique: −9-9, 00, −5-5, and 99 all map to distinct outputs. Therefore, this set is a function.

The correct answer is: {(−9,0),(0,0),(−5,−2),(9,2)}\{(-9, 0), (0, 0), (-5, -2), (9, 2)\}

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Math Problem Analysis

Mathematical Concepts

Relations and Functions
Ordered Pairs
Unique Mapping

Formulas

Definition of a function: each input must have a unique output

Theorems

Function uniqueness property

Suitable Grade Level

Grades 7-9

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