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Sagot :
To determine which of the given tables represent one-to-one functions, we need to analyze the [tex]\( y \)[/tex]-values in each table. A function is one-to-one if every [tex]\( y \)[/tex]-value is unique, meaning no two [tex]\( x \)[/tex]-values map to the same [tex]\( y \)[/tex]-value. Let's examine each table individually.
### Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -1 & 1 & 5 & 8 \\ \hline \end{array} \][/tex]
For Table 1, the [tex]\( y \)[/tex]-values are [tex]\(-1, 1, 5, 8\)[/tex]. Since all the [tex]\( y \)[/tex]-values are unique, this table represents a one-to-one function.
### Table 2:
[tex]\[ \begin{array}{|l|r|r|r|r|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -16 & -6 & 14 & 29 \\ \hline \end{array} \][/tex]
For Table 2, the [tex]\( y \)[/tex]-values are [tex]\(-16, -6, 14, 29\)[/tex]. Since all the [tex]\( y \)[/tex]-values are unique, this table also represents a one-to-one function.
### Table 3:
[tex]\[ \begin{array}{|l|r|r|r|r|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & 16 & 4 & 4 & 25 \\ \hline \end{array} \][/tex]
For Table 3, the [tex]\( y \)[/tex]-values are [tex]\( 16, 4, 4, 25 \)[/tex]. Since the [tex]\( y \)[/tex]-value [tex]\( 4 \)[/tex] is repeated, this table does not represent a one-to-one function.
### Table 4:
[tex]\[ \begin{array}{|l|r|r|r|r|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -16 & -6 & -6 & 29 \\ \hline \end{array} \][/tex]
For Table 4, the [tex]\( y \)[/tex]-values are [tex]\( -16, -6, -6, 29 \)[/tex]. Since the [tex]\( y \)[/tex]-value [tex]\( -6 \)[/tex] is repeated, this table does not represent a one-to-one function.
### Conclusion
The tables that represent one-to-one functions are:
1.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -1 & 1 & 5 & 8 \\ \hline \end{array} \][/tex]
2.
[tex]\[ \begin{array}{|l|r|r|r|r|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -16 & -6 & 14 & 29 \\ \hline \end{array} \][/tex]
Therefore, the tables corresponding to one-to-one functions are tables 1 and 2.
### Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -1 & 1 & 5 & 8 \\ \hline \end{array} \][/tex]
For Table 1, the [tex]\( y \)[/tex]-values are [tex]\(-1, 1, 5, 8\)[/tex]. Since all the [tex]\( y \)[/tex]-values are unique, this table represents a one-to-one function.
### Table 2:
[tex]\[ \begin{array}{|l|r|r|r|r|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -16 & -6 & 14 & 29 \\ \hline \end{array} \][/tex]
For Table 2, the [tex]\( y \)[/tex]-values are [tex]\(-16, -6, 14, 29\)[/tex]. Since all the [tex]\( y \)[/tex]-values are unique, this table also represents a one-to-one function.
### Table 3:
[tex]\[ \begin{array}{|l|r|r|r|r|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & 16 & 4 & 4 & 25 \\ \hline \end{array} \][/tex]
For Table 3, the [tex]\( y \)[/tex]-values are [tex]\( 16, 4, 4, 25 \)[/tex]. Since the [tex]\( y \)[/tex]-value [tex]\( 4 \)[/tex] is repeated, this table does not represent a one-to-one function.
### Table 4:
[tex]\[ \begin{array}{|l|r|r|r|r|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -16 & -6 & -6 & 29 \\ \hline \end{array} \][/tex]
For Table 4, the [tex]\( y \)[/tex]-values are [tex]\( -16, -6, -6, 29 \)[/tex]. Since the [tex]\( y \)[/tex]-value [tex]\( -6 \)[/tex] is repeated, this table does not represent a one-to-one function.
### Conclusion
The tables that represent one-to-one functions are:
1.
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -1 & 1 & 5 & 8 \\ \hline \end{array} \][/tex]
2.
[tex]\[ \begin{array}{|l|r|r|r|r|} \hline x & -4 & -2 & 2 & 5 \\ \hline y & -16 & -6 & 14 & 29 \\ \hline \end{array} \][/tex]
Therefore, the tables corresponding to one-to-one functions are tables 1 and 2.
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