Select the correct answer.
State the domain and range of the following function.
$\left\{(2,3),(7,9),(4,-7),(6,2),(3,-5)\right\}$
A. Domain: $\{-7,-5,2,3,7\}$; Range: $\{2,4,6,9\}$
B. Domain: $\{2,2,3,4,7\}$; Range: $\{-7,-5,2,9,3\}$
C. Domain: $\{2,3,4,6,7\}$; Range: $\{-7,-5,2,3,9\}$
D. Domain: $\{-7,-5,2,3,9\}$; Range: $\{2,3,4,6,7\}$
Answer (1)
The domain consists of the first elements of the ordered pairs: {2, 3, 4, 6, 7}.
The range consists of the second elements of the ordered pairs: {-7, -5, 2, 3, 9}.
Match the calculated domain and range with the options.
The correct answer is C: Domain: {2, 3, 4, 6, 7}; Range: {-7, -5, 2, 3, 9}. C
Explanation
Understanding Domain and Range We are given a function as a set of ordered pairs:
{( 2 , 3 ) , ( 7 , 9 ) , ( 4 , − 7 ) , ( 6 , 2 ) , ( 3 , − 5 )}
The domain of the function is the set of all first elements in the ordered pairs, and the range is the set of all second elements in the ordered pairs. We need to identify the correct domain and range from the given options.
Finding the Domain Let's list the first elements (x-values) of the ordered pairs:
2 , 7 , 4 , 6 , 3
The domain is the set of these elements. We write it in set notation, removing any duplicates and ordering the elements:
{ 2 , 3 , 4 , 6 , 7 }
Finding the Range Now, let's list the second elements (y-values) of the ordered pairs:
3 , 9 , − 7 , 2 , − 5
The range is the set of these elements. We write it in set notation, removing any duplicates and ordering the elements:
{ − 7 , − 5 , 2 , 3 , 9 }
Selecting the Correct Answer Comparing our calculated domain and range with the given options:
A. Domain: { − 7 , − 5 , 2 , 3 , 7 } ; Range: { 2 , 4 , 6 , 9 }
B. Domain: { 2 , 2 , 3 , 4 , 7 } ; Range: { − 7 , − 5 , 2 , 9 , 3 }
C. Domain: { 2 , 3 , 4 , 6 , 7 } ; Range: { − 7 , − 5 , 2 , 3 , 9 }
D. Domain: { − 7 , − 5 , 2 , 3 , 9 } ; Range: { 2 , 3 , 4 , 6 , 7 }
Option C matches our calculated domain and range.
Final Answer Therefore, the correct answer is:
Domain: { 2 , 3 , 4 , 6 , 7 } ; Range: { − 7 , − 5 , 2 , 3 , 9 }
Examples
Understanding domain and range is crucial in many real-world applications. For instance, if you're tracking the performance of a stock over time, the domain could represent the days you're observing, and the range could represent the stock prices on those days. Similarly, in a science experiment, the domain might be the different temperatures at which you measure a reaction rate, and the range would be the reaction rates themselves. Knowing the domain and range helps you understand the boundaries and possible values of the data you're working with.
