Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Let's analyze the two given relations, [tex]\( R \)[/tex] and [tex]\( Q \)[/tex], step by step to find their domains and ranges.
Relation [tex]\( R \)[/tex]:
We are provided with a table of values for relation [tex]\( R \)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -3 & 5 \\ \hline -1 & 2 \\ \hline 1 & -1 \\ \hline -1 & 4 \\ \hline \end{tabular} \][/tex]
1. Domain of [tex]\( R \)[/tex]: The domain of a relation is the set of all unique [tex]\( x \)[/tex]-values.
From the table, the [tex]\( x \)[/tex]-values are: [tex]\(-3, -1, 1, -1\)[/tex].
After removing duplicates, we get the domain: [tex]\(\{-3, -1, 1\}\)[/tex].
2. Range of [tex]\( R \)[/tex]: The range of a relation is the set of all unique [tex]\( y \)[/tex]-values.
From the table, the [tex]\( y \)[/tex]-values are: [tex]\(5, 2, -1, 4\)[/tex].
There are no duplicates, so the range is: [tex]\(\{5, 2, -1, 4\}\)[/tex].
Thus, for relation [tex]\( R \)[/tex], the domain and range are:
- Domain of [tex]\( R \)[/tex]: [tex]\(\{1, -3, -1\}\)[/tex] (Note: Set notation orders elements uniquely, hence ordering may vary)
- Range of [tex]\( R \)[/tex]: [tex]\(\{2, 4, 5, -1\}\)[/tex]
Relation [tex]\( Q \)[/tex]:
Relation [tex]\( Q \)[/tex] is given as a list of ordered pairs:
[tex]\[ Q = \{(-2,4), (0,2), (-1,3), (4,-2)\} \][/tex]
1. Domain of [tex]\( Q \)[/tex]: The domain of a relation is the set of all unique [tex]\( x \)[/tex]-values.
From the ordered pairs, the [tex]\( x \)[/tex]-values are: [tex]\(-2, 0, -1, 4\)[/tex].
So, the domain is: [tex]\(\{-2, 0, -1, 4\}\)[/tex].
2. Range of [tex]\( Q \)[/tex]: The range of a relation is the set of all unique [tex]\( y \)[/tex]-values.
From the ordered pairs, the [tex]\( y \)[/tex]-values are: [tex]\(4, 2, 3, -2\)[/tex].
So, the range is: [tex]\(\{4, 2, 3, -2\}\)[/tex].
Thus, for relation [tex]\( Q \)[/tex], the domain and range are:
- Domain of [tex]\( Q \)[/tex]: [tex]\(\{0, 4, -2, -1\}\)[/tex] (Note: Set notation orders elements uniquely, hence ordering may vary)
- Range of [tex]\( Q \)[/tex]: [tex]\(\{2, 3, 4, -2\}\)[/tex]
To summarize everything together:
- Domain of [tex]\( R \)[/tex]: [tex]\(\{1, -3, -1\}\)[/tex]
- Range of [tex]\( R \)[/tex]: [tex]\(\{2, 4, 5, -1\}\)[/tex]
- Domain of [tex]\( Q \)[/tex]: [tex]\(\{0, 4, -2, -1\}\)[/tex]
- Range of [tex]\( Q \)[/tex]: [tex]\(\{2, 3, 4, -2\}\)[/tex]
Relation [tex]\( R \)[/tex]:
We are provided with a table of values for relation [tex]\( R \)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -3 & 5 \\ \hline -1 & 2 \\ \hline 1 & -1 \\ \hline -1 & 4 \\ \hline \end{tabular} \][/tex]
1. Domain of [tex]\( R \)[/tex]: The domain of a relation is the set of all unique [tex]\( x \)[/tex]-values.
From the table, the [tex]\( x \)[/tex]-values are: [tex]\(-3, -1, 1, -1\)[/tex].
After removing duplicates, we get the domain: [tex]\(\{-3, -1, 1\}\)[/tex].
2. Range of [tex]\( R \)[/tex]: The range of a relation is the set of all unique [tex]\( y \)[/tex]-values.
From the table, the [tex]\( y \)[/tex]-values are: [tex]\(5, 2, -1, 4\)[/tex].
There are no duplicates, so the range is: [tex]\(\{5, 2, -1, 4\}\)[/tex].
Thus, for relation [tex]\( R \)[/tex], the domain and range are:
- Domain of [tex]\( R \)[/tex]: [tex]\(\{1, -3, -1\}\)[/tex] (Note: Set notation orders elements uniquely, hence ordering may vary)
- Range of [tex]\( R \)[/tex]: [tex]\(\{2, 4, 5, -1\}\)[/tex]
Relation [tex]\( Q \)[/tex]:
Relation [tex]\( Q \)[/tex] is given as a list of ordered pairs:
[tex]\[ Q = \{(-2,4), (0,2), (-1,3), (4,-2)\} \][/tex]
1. Domain of [tex]\( Q \)[/tex]: The domain of a relation is the set of all unique [tex]\( x \)[/tex]-values.
From the ordered pairs, the [tex]\( x \)[/tex]-values are: [tex]\(-2, 0, -1, 4\)[/tex].
So, the domain is: [tex]\(\{-2, 0, -1, 4\}\)[/tex].
2. Range of [tex]\( Q \)[/tex]: The range of a relation is the set of all unique [tex]\( y \)[/tex]-values.
From the ordered pairs, the [tex]\( y \)[/tex]-values are: [tex]\(4, 2, 3, -2\)[/tex].
So, the range is: [tex]\(\{4, 2, 3, -2\}\)[/tex].
Thus, for relation [tex]\( Q \)[/tex], the domain and range are:
- Domain of [tex]\( Q \)[/tex]: [tex]\(\{0, 4, -2, -1\}\)[/tex] (Note: Set notation orders elements uniquely, hence ordering may vary)
- Range of [tex]\( Q \)[/tex]: [tex]\(\{2, 3, 4, -2\}\)[/tex]
To summarize everything together:
- Domain of [tex]\( R \)[/tex]: [tex]\(\{1, -3, -1\}\)[/tex]
- Range of [tex]\( R \)[/tex]: [tex]\(\{2, 4, 5, -1\}\)[/tex]
- Domain of [tex]\( Q \)[/tex]: [tex]\(\{0, 4, -2, -1\}\)[/tex]
- Range of [tex]\( Q \)[/tex]: [tex]\(\{2, 3, 4, -2\}\)[/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
