Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
