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Sagot :
To solve this problem, we need to match each table to its corresponding equation.
We are given the following equations:
1. [tex]\( y = x \)[/tex]
2. [tex]\( y = \sqrt{x} \)[/tex]
3. [tex]\( y = \frac{1}{x} \)[/tex]
4. [tex]\( y = x^2 \)[/tex]
5. [tex]\( y = x^3 \)[/tex]
6. [tex]\( y = |x| \)[/tex]
Let's analyze each table:
Table a:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & 2 \\ \hline -1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline 3 & 3 \\ \hline \end{tabular} \][/tex]
For table a:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = 2 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 2 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( y = 3 \)[/tex]
This table corresponds to the equation [tex]\( y = |x| \)[/tex].
Table b:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & - \\ \hline -1 & - \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 4 & 2 \\ \hline 9 & 3 \\ \hline \end{tabular} \][/tex]
For table b, only non-negative inputs have defined outputs:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 4 \)[/tex], [tex]\( y = 2 \)[/tex]
- When [tex]\( x = 9 \)[/tex], [tex]\( y = 3 \)[/tex]
This table corresponds to the equation [tex]\( y = \sqrt{x} \)[/tex].
Table c:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & -8 \\ \hline -1 & -1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 8 \\ \hline 3 & 27 \\ \hline \end{tabular} \][/tex]
For table c:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = -8 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = -1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 8 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( y = 27 \)[/tex]
This table corresponds to the equation [tex]\( y = x^3 \)[/tex].
Table d:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & -0.5 \\ \hline -1 & -1 \\ \hline 0 & - \\ \hline 1 & 1 \\ \hline 2 & 0.5 \\ \hline 3 & 0.33 \\ \hline \end{tabular} \][/tex]
For table d:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = -0.5 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = -1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y \)[/tex] is undefined
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 0.5 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( y = 0.33 \)[/tex]
This table corresponds to the equation [tex]\( y = \frac{1}{x} \)[/tex].
Table e:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & -2 \\ \hline -1 & -1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline 3 & 3 \\ \hline \end{tabular} \][/tex]
For table e:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = -2 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = -1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 2 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( y = 3 \)[/tex]
This table corresponds to the equation [tex]\( y = x \)[/tex].
Table f:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & 4 \\ \hline -1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 4 \\ \hline \end{tabular} \][/tex]
For table f:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = 4 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 4 \)[/tex]
This table corresponds to the equation [tex]\( y = x^2 \)[/tex].
Hence, the matching is:
- [tex]\( y = x \)[/tex]: Table e
- [tex]\( y = \sqrt{x} \)[/tex]: Table b
- [tex]\( y = \frac{1}{x} \)[/tex]: Table d
- [tex]\( y = x^2 \)[/tex]: Table f
- [tex]\( y = x^3 \)[/tex]: Table c
- [tex]\( y = |x| \)[/tex]: Table a
We are given the following equations:
1. [tex]\( y = x \)[/tex]
2. [tex]\( y = \sqrt{x} \)[/tex]
3. [tex]\( y = \frac{1}{x} \)[/tex]
4. [tex]\( y = x^2 \)[/tex]
5. [tex]\( y = x^3 \)[/tex]
6. [tex]\( y = |x| \)[/tex]
Let's analyze each table:
Table a:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & 2 \\ \hline -1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline 3 & 3 \\ \hline \end{tabular} \][/tex]
For table a:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = 2 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 2 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( y = 3 \)[/tex]
This table corresponds to the equation [tex]\( y = |x| \)[/tex].
Table b:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & - \\ \hline -1 & - \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 4 & 2 \\ \hline 9 & 3 \\ \hline \end{tabular} \][/tex]
For table b, only non-negative inputs have defined outputs:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 4 \)[/tex], [tex]\( y = 2 \)[/tex]
- When [tex]\( x = 9 \)[/tex], [tex]\( y = 3 \)[/tex]
This table corresponds to the equation [tex]\( y = \sqrt{x} \)[/tex].
Table c:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & -8 \\ \hline -1 & -1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 8 \\ \hline 3 & 27 \\ \hline \end{tabular} \][/tex]
For table c:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = -8 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = -1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 8 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( y = 27 \)[/tex]
This table corresponds to the equation [tex]\( y = x^3 \)[/tex].
Table d:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & -0.5 \\ \hline -1 & -1 \\ \hline 0 & - \\ \hline 1 & 1 \\ \hline 2 & 0.5 \\ \hline 3 & 0.33 \\ \hline \end{tabular} \][/tex]
For table d:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = -0.5 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = -1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y \)[/tex] is undefined
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 0.5 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( y = 0.33 \)[/tex]
This table corresponds to the equation [tex]\( y = \frac{1}{x} \)[/tex].
Table e:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & -2 \\ \hline -1 & -1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline 3 & 3 \\ \hline \end{tabular} \][/tex]
For table e:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = -2 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = -1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 2 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( y = 3 \)[/tex]
This table corresponds to the equation [tex]\( y = x \)[/tex].
Table f:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & 4 \\ \hline -1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 4 \\ \hline \end{tabular} \][/tex]
For table f:
- When [tex]\( x = -2 \)[/tex], [tex]\( y = 4 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 0 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( y = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 4 \)[/tex]
This table corresponds to the equation [tex]\( y = x^2 \)[/tex].
Hence, the matching is:
- [tex]\( y = x \)[/tex]: Table e
- [tex]\( y = \sqrt{x} \)[/tex]: Table b
- [tex]\( y = \frac{1}{x} \)[/tex]: Table d
- [tex]\( y = x^2 \)[/tex]: Table f
- [tex]\( y = x^3 \)[/tex]: Table c
- [tex]\( y = |x| \)[/tex]: Table a
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