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Question 11 (Multiple Choice Worth 2 points)

Which of the following sets of ordered pairs represents a function?

A. [tex]\{(-3, -3), (-2, -2), (-1, -1), (0, 0), (1, 1)\}[/tex]

B. [tex]\{(-3, -3), (-3, -2), (-3, -1), (-3, 0), (-4, -1)\}[/tex]

C. [tex]\{(-3, -3), (-3, -1), (-1, -2), (-1, -1), (-1, 0)\}[/tex]

D. [tex]\{(-3, -3), (-3, 0), (-1, -3), (0, -3), (-1, -1)\}[/tex]


Sagot :

To determine which of the given sets of ordered pairs represents a function, we need to recall the definition of a function. In the context of ordered pairs, a set represents a function if and only if each input (or [tex]\(x\)[/tex]-value) is associated with exactly one output (or [tex]\(y\)[/tex]-value). This means that no [tex]\(x\)[/tex]-value should be repeated with different [tex]\(y\)[/tex]-values.

We will analyze each set of ordered pairs provided in the options.

1. Set 1: [tex]\(\{(-3,-3),(-2,-2),(-1,-1),(0,0),(1,1)\}\)[/tex]

[tex]\[ \begin{aligned} &\text{The x-values are:} \{-3, -2, -1, 0, 1\} \\ &\text{All x-values are unique.} \\ &\text{Therefore, each x-value maps to exactly one y-value.} \end{aligned} \][/tex]
This set represents a function.

2. Set 2: [tex]\(\{(-3,-3),(-3,-2),(-3,-1),(-3,0),(-4,-1)\}\)[/tex]

[tex]\[ \begin{aligned} &\text{The x-values are:} \{-3, -3, -3, -3, -4\} \\ &\text{The x-value } -3 \text{ is repeated multiple times with different } y\text{-values}. \end{aligned} \][/tex]
This set does not represent a function because the x-value -3 is not unique; it corresponds to multiple y-values.

3. Set 3: [tex]\(\{(-3,-3),(-3,-1),(-1,-2),(-1,-1),(-1,0)\}\)[/tex]

[tex]\[ \begin{aligned} &\text{The x-values are:} \{-3, -3, -1, -1, -1\} \\ &\text{The x-values } -3 \text{ and } -1 \text{ are repeated with different } y\text{-values}. \end{aligned} \][/tex]
This set does not represent a function because both -3 and -1 have multiple corresponding y-values.

4. Set 4: [tex]\(\{(-3,-3),(-3,0),(-1,-3),(0,-3),(-1,-1)\}\)[/tex]

[tex]\[ \begin{aligned} &\text{The x-values are:} \{-3, -3, -1, 0, -1\} \\ &\text{The x-values } -3 \text{ and } -1 \text{ are repeated with different } y\text{-values}. \end{aligned} \][/tex]
This set does not represent a function because the x-values -3 and -1 are not unique; they appear multiple times with different y-values.

Based on the above analysis, the set of ordered pairs that represents a function is:

[tex]\[ \{(-3,-3),(-2,-2),(-1,-1),(0,0),(1,1)\} \][/tex]

So, the correct answer is the first set of ordered pairs.
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