Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To determine which table represents a function, we need to check each table for the definition of a function. A function is such that for every [tex]\( x \)[/tex]-value, there must be exactly one [tex]\( y \)[/tex]-value. In other words, each [tex]\( x \)[/tex]-value should map to a unique [tex]\( y \)[/tex]-value.
Let's review each table one by one:
### Table 1:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3 & -1 \\ \hline 0 & 0 \\ \hline -2 & -1 \\ \hline 8 & 1 \\ \hline \end{array} \][/tex]
In this table:
- [tex]\( x = -3 \)[/tex] maps to [tex]\( y = -1 \)[/tex]
- [tex]\( x = 0 \)[/tex] maps to [tex]\( y = 0 \)[/tex]
- [tex]\( x = -2 \)[/tex] maps to [tex]\( y = -1 \)[/tex]
- [tex]\( x = 8 \)[/tex] maps to [tex]\( y = 1 \)[/tex]
Each [tex]\( x \)[/tex]-value is unique and maps to only one [tex]\( y \)[/tex]-value. Thus, this table represents a function.
### Table 2:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -5 & -5 \\ \hline 0 & 0 \\ \hline -5 & 5 \\ \hline 6 & -6 \\ \hline \end{array} \][/tex]
In this table:
- [tex]\( x = -5 \)[/tex] maps to [tex]\( y = -5 \)[/tex]
- [tex]\( x = 0 \)[/tex] maps to [tex]\( y = 0 \)[/tex]
- [tex]\( x = -5 \)[/tex] also maps to [tex]\( y = 5 \)[/tex]
- [tex]\( x = 6 \)[/tex] maps to [tex]\( y = -6 \)[/tex]
The [tex]\( x \)[/tex]-value [tex]\( -5 \)[/tex] maps to two different [tex]\( y \)[/tex]-values (-5 and 5). Thus, this table does not represent a function.
### Table 3:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -4 & 8 \\ \hline -2 & 2 \\ \hline -2 & 4 \\ \hline 0 & 2 \\ \hline \end{array} \][/tex]
In this table:
- [tex]\( x = -4 \)[/tex] maps to [tex]\( y = 8 \)[/tex]
- [tex]\( x = -2 \)[/tex] maps to [tex]\( y = 2 \)[/tex]
- [tex]\( x = -2 \)[/tex] also maps to [tex]\( y = 4 \)[/tex]
- [tex]\( x = 0 \)[/tex] maps to [tex]\( y = 2 \)[/tex]
The [tex]\( x \)[/tex]-value [tex]\( -2 \)[/tex] maps to two different [tex]\( y \)[/tex]-values (2 and 4). Thus, this table does not represent a function.
### Table 4:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -4 & 2 \\ \hline 3 & 5 \\ \hline 1 & 3 \\ \hline -4 & 0 \\ \hline \end{array} \][/tex]
In this table:
- [tex]\( x = -4 \)[/tex] maps to [tex]\( y = 2 \)[/tex]
- [tex]\( x = 3 \)[/tex] maps to [tex]\( y = 5 \)[/tex]
- [tex]\( x = 1 \)[/tex] maps to [tex]\( y = 3 \)[/tex]
- [tex]\( x = -4 \)[/tex] also maps to [tex]\( y = 0 \)[/tex]
The [tex]\( x \)[/tex]-value [tex]\( -4 \)[/tex] maps to two different [tex]\( y \)[/tex]-values (2 and 0). Thus, this table does not represent a function.
### Conclusion:
Only Table 1 represents a function.
Let's review each table one by one:
### Table 1:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3 & -1 \\ \hline 0 & 0 \\ \hline -2 & -1 \\ \hline 8 & 1 \\ \hline \end{array} \][/tex]
In this table:
- [tex]\( x = -3 \)[/tex] maps to [tex]\( y = -1 \)[/tex]
- [tex]\( x = 0 \)[/tex] maps to [tex]\( y = 0 \)[/tex]
- [tex]\( x = -2 \)[/tex] maps to [tex]\( y = -1 \)[/tex]
- [tex]\( x = 8 \)[/tex] maps to [tex]\( y = 1 \)[/tex]
Each [tex]\( x \)[/tex]-value is unique and maps to only one [tex]\( y \)[/tex]-value. Thus, this table represents a function.
### Table 2:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -5 & -5 \\ \hline 0 & 0 \\ \hline -5 & 5 \\ \hline 6 & -6 \\ \hline \end{array} \][/tex]
In this table:
- [tex]\( x = -5 \)[/tex] maps to [tex]\( y = -5 \)[/tex]
- [tex]\( x = 0 \)[/tex] maps to [tex]\( y = 0 \)[/tex]
- [tex]\( x = -5 \)[/tex] also maps to [tex]\( y = 5 \)[/tex]
- [tex]\( x = 6 \)[/tex] maps to [tex]\( y = -6 \)[/tex]
The [tex]\( x \)[/tex]-value [tex]\( -5 \)[/tex] maps to two different [tex]\( y \)[/tex]-values (-5 and 5). Thus, this table does not represent a function.
### Table 3:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -4 & 8 \\ \hline -2 & 2 \\ \hline -2 & 4 \\ \hline 0 & 2 \\ \hline \end{array} \][/tex]
In this table:
- [tex]\( x = -4 \)[/tex] maps to [tex]\( y = 8 \)[/tex]
- [tex]\( x = -2 \)[/tex] maps to [tex]\( y = 2 \)[/tex]
- [tex]\( x = -2 \)[/tex] also maps to [tex]\( y = 4 \)[/tex]
- [tex]\( x = 0 \)[/tex] maps to [tex]\( y = 2 \)[/tex]
The [tex]\( x \)[/tex]-value [tex]\( -2 \)[/tex] maps to two different [tex]\( y \)[/tex]-values (2 and 4). Thus, this table does not represent a function.
### Table 4:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -4 & 2 \\ \hline 3 & 5 \\ \hline 1 & 3 \\ \hline -4 & 0 \\ \hline \end{array} \][/tex]
In this table:
- [tex]\( x = -4 \)[/tex] maps to [tex]\( y = 2 \)[/tex]
- [tex]\( x = 3 \)[/tex] maps to [tex]\( y = 5 \)[/tex]
- [tex]\( x = 1 \)[/tex] maps to [tex]\( y = 3 \)[/tex]
- [tex]\( x = -4 \)[/tex] also maps to [tex]\( y = 0 \)[/tex]
The [tex]\( x \)[/tex]-value [tex]\( -4 \)[/tex] maps to two different [tex]\( y \)[/tex]-values (2 and 0). Thus, this table does not represent a function.
### Conclusion:
Only Table 1 represents a function.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
