Questions: Relations and Functions Assignment Active Find the Domain and Range of Relations The relation R is shown in the table below. x y -3 5 -1 2 1 -1 -1 4 Domain: Range: The relation Q is described as a list of ordered pairs, shown below. Q=(-2,4),(0,2),(-1,3),(4,-2)

Relations and Functions Assignment Active Find the Domain and Range of Relations The relation R is shown in the table below. x y -3 5 -1 2 1 -1 -1 4 Domain: Range: The relation Q is described as a list of ordered pairs, shown below. Q=(-2,4),(0,2),(-1,3),(4,-2)
Transcript text: Relations and Functions Assignment Active Find the Domain and Range of Relations The relation $R$ is shown in the table below. \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline-3 & 5 \\ \hline-1 & 2 \\ \hline 1 & -1 \\ \hline-1 & 4 \\ \hline \end{tabular} Domain: Range: The relation $Q$ is described as a list of ordered pairs, shown below. \[ Q=\{(-2,4),(0,2),(-1,3),(4,-2)\} \]
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Solution

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Solution Steps

Step 1: Find the domain of relation R

The domain of a relation is the set of all possible x-values. In the given table for relation R, the x-values are -3, -1, 1, and -1. Since -1 appears twice, we only list it once in the set. Therefore, the domain of R is \(\{-3, -1, 1\}\).

Step 2: Find the range of relation R

The range of a relation is the set of all possible y-values. In the given table for relation R, the y-values are 5, 2, -1, and 4. Therefore, the range of R is \(\{5, 2, -1, 4\}\).

Step 3: Find the domain of relation Q

The domain of relation Q is the set of the first elements in each ordered pair. The ordered pairs are (-2, 4), (0, 2), (-1, 3), and (4, -2). The first elements are -2, 0, -1, and 4. Therefore, the domain of relation Q is \(\{-2, 0, -1, 4\}\).

Step 4: Find the range of relation Q

The range of relation Q is the set of the second elements in each ordered pair. The ordered pairs are (-2, 4), (0, 2), (-1, 3), and (4, -2). The second elements are 4, 2, 3, and -2. Therefore, the range of relation Q is \(\{4, 2, 3, -2\}\).

Final Answer

Domain of R: \(\boxed{\{-3, -1, 1\}}\) Range of R: \(\boxed{\{-1, 2, 4, 5\}}\) Domain of Q: \(\boxed{\{-2, 0, -1, 4\}}\) Range of Q: \(\boxed{\{-2, 2, 3, 4\}}\)

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