Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Let's carefully analyze each option to determine which one represents a function.
Definition of a function:
A function is a relation in which each element of the domain (all possible [tex]\(x\)[/tex]-values) is paired with exactly one element of the range (all possible [tex]\(y\)[/tex]-values). This means that no [tex]\(x\)[/tex]-value should be repeated with a different [tex]\(y\)[/tex]-value.
### Option A
[tex]\[ \begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 5 & -5 & 10 & 5 & -10 \\ \hline $y$ & 13 & -7 & 23 & 17 & -17 \\ \hline \end{tabular} \][/tex]
In this table, the [tex]\(x\)[/tex]-value 5 is associated with both 13 and 17. Since one [tex]\(x\)[/tex]-value maps to two different [tex]\(y\)[/tex]-values, this option does not represent a function.
### Option B
[tex]\[ \{(0, 2), (2, 0), (4, 3)\} \][/tex]
Here, each [tex]\(x\)[/tex]-value (0, 2, and 4) is paired with exactly one unique [tex]\(y\)[/tex]-value. There are no repeated [tex]\(x\)[/tex]-values with different [tex]\(y\)[/tex]-values. Therefore, this option represents a function.
### Option C
There is no Option C provided in the text.
### Option D
[tex]\[ \{(-7, -9), (-4, -9), (5, 15), (7, 19)\} \][/tex]
In this set, each [tex]\(x\)[/tex]-value (-7, -4, 5, and 7) is paired with exactly one unique [tex]\(y\)[/tex]-value. No [tex]\(x\)[/tex]-value is repeated here, which means this option also represents a function.
### Summary
Based on the given options, we find that:
- Option A is not a function because the [tex]\(x\)[/tex]-value 5 is associated with more than one [tex]\(y\)[/tex]-value.
- Option B is a function as each [tex]\(x\)[/tex]-value has a unique [tex]\(y\)[/tex]-value.
- Option D is also a function for the same reason.
Since we need to select one correct answer, we conclude that:
The correct answer is Option B.
Definition of a function:
A function is a relation in which each element of the domain (all possible [tex]\(x\)[/tex]-values) is paired with exactly one element of the range (all possible [tex]\(y\)[/tex]-values). This means that no [tex]\(x\)[/tex]-value should be repeated with a different [tex]\(y\)[/tex]-value.
### Option A
[tex]\[ \begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 5 & -5 & 10 & 5 & -10 \\ \hline $y$ & 13 & -7 & 23 & 17 & -17 \\ \hline \end{tabular} \][/tex]
In this table, the [tex]\(x\)[/tex]-value 5 is associated with both 13 and 17. Since one [tex]\(x\)[/tex]-value maps to two different [tex]\(y\)[/tex]-values, this option does not represent a function.
### Option B
[tex]\[ \{(0, 2), (2, 0), (4, 3)\} \][/tex]
Here, each [tex]\(x\)[/tex]-value (0, 2, and 4) is paired with exactly one unique [tex]\(y\)[/tex]-value. There are no repeated [tex]\(x\)[/tex]-values with different [tex]\(y\)[/tex]-values. Therefore, this option represents a function.
### Option C
There is no Option C provided in the text.
### Option D
[tex]\[ \{(-7, -9), (-4, -9), (5, 15), (7, 19)\} \][/tex]
In this set, each [tex]\(x\)[/tex]-value (-7, -4, 5, and 7) is paired with exactly one unique [tex]\(y\)[/tex]-value. No [tex]\(x\)[/tex]-value is repeated here, which means this option also represents a function.
### Summary
Based on the given options, we find that:
- Option A is not a function because the [tex]\(x\)[/tex]-value 5 is associated with more than one [tex]\(y\)[/tex]-value.
- Option B is a function as each [tex]\(x\)[/tex]-value has a unique [tex]\(y\)[/tex]-value.
- Option D is also a function for the same reason.
Since we need to select one correct answer, we conclude that:
The correct answer is Option B.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.