Select the correct answer.
$\begin{array}{c}
(-1,1) \\
(0,-1) \\
(5,-11) \\
(10,-21)
\end{array}$
What is the domain of the set of ordered pairs above?
A. $\{-1,0,5,10\}$
B. $\{-1,10\}$
C. $\{1,-1,-11,-21\}$
D. $\{-1,1\}$
Answer (2)
Identify the first element of each ordered pair.
List the set of all first elements: { − 1 , 0 , 5 , 10 } .
The resulting set is the domain.
The domain of the set of ordered pairs is { − 1 , 0 , 5 , 10 } .
Explanation
Understanding the Domain We are given a set of ordered pairs: ( − 1 , 1 ) , ( 0 , − 1 ) , ( 5 , − 11 ) , and ( 10 , − 21 ) . The domain of a set of ordered pairs is the set of all the first elements (x-coordinates) in those pairs. Our goal is to identify these first elements and list them as the domain.
Identifying the First Elements Let's extract the first elements from each ordered pair:
From ( − 1 , 1 ) , the first element is − 1 .
From ( 0 , − 1 ) , the first element is 0 .
From ( 5 , − 11 ) , the first element is 5 .
From ( 10 , − 21 ) , the first element is 10 .
Constructing the Domain Set Now, we create a set containing these first elements: { − 1 , 0 , 5 , 10 } . This set represents the domain of the given set of ordered pairs.
Selecting the Correct Answer Comparing our result with the given options, we see that option A, { − 1 , 0 , 5 , 10 } , matches our calculated domain. Therefore, the correct answer is A.
Examples
Understanding the domain is crucial in many real-world applications. For instance, if you're tracking the temperature at different times of the day, the times at which you take the measurements form the domain. Similarly, if you're analyzing the performance of a stock over several days, the dates you're considering constitute the domain. Knowing the domain helps you define the scope of your analysis and ensures you're working with relevant data.
The domain of the set of ordered pairs, which consists of the first elements, is {-1, 0, 5, 10}. Therefore, the correct answer is A. This set represents all unique x-coordinates from the ordered pairs given.
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