Answered

Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function?

Select all that apply:

A. [tex]$\{(4,9),(0,-2),(0,2),(5,4)\}$[/tex]
B. [tex]$\{(5,-5),(5,-4),(7,-2),(3,8)\}$[/tex]
C. [tex]$\{(4,3),(8,0),(5,2),(-5,0)\}$[/tex]
D. [tex]$\{(6,9),(9,-4),(6,1),(-5,11)\}$[/tex]
E. [tex]$\{(4,12),(2,6),(-5,6),(3,-2)\}$[/tex]



Answer :

GinnyAnswer
To determine in which sets the given relations represent a function, we need to verify if each relation maintains the definition of a function: that for every element [tex]\( x \)[/tex] in the domain, there should be exactly one corresponding element [tex]\( y \)[/tex] in the co-domain.

Let's analyze the relations one by one:

1. [tex]\(\{(4, 9), (0, -2), (0, 2), (5, 4)\}\)[/tex]

- Here, [tex]\( 0 \)[/tex] is associated with both [tex]\(-2\)[/tex] and [tex]\(2\)[/tex]. Therefore, this relation is not a function.

2. [tex]\(\{(5, -5), (5, -4), (7, -2), (3, 8)\}\)[/tex]

- Here, [tex]\( 5 \)[/tex] is associated with both [tex]\(-5\)[/tex] and [tex]\(-4\)[/tex]. Therefore, this relation is not a function.

3. [tex]\(\{(4, 3), (8, 0), (5, 2), (-5, 0)\}\)[/tex]

- Here, each [tex]\( x \)[/tex] value (4, 8, 5, -5) is unique and appears only once in the domain. Therefore, this relation is a function.

4. [tex]\(\{(6, 9), (9, -4), (6, 1), (-5, 11)\}\)[/tex]

- Here, [tex]\( 6 \)[/tex] is associated with both [tex]\(9\)[/tex] and [tex]\(1\)[/tex]. Therefore, this relation is not a function.

5. [tex]\(\{(4, 12), (2, 6), (-5, 6), (3, -2)\}\)[/tex]

- Each [tex]\( x \)[/tex] value (4, 2, -5, 3) is unique and appears only once in the domain. Therefore, this relation is a function.

Based on this analysis, the relations that are functions are:

[tex]\[ \{(4, 3), (8, 0), (5, 2), (-5, 0)\} \{(4, 12), (2, 6), (-5, 6), (3, -2)\} \][/tex]

Therefore, the correct answer is:

[tex]\([3, 5]\)[/tex]

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