Select the correct answer.
State the domain and range of the following function.
$\left\{(6,-8),(9,3),(-3,5),(1,-6),(5,7)\right\}$
A. Domain: $\{-3,1,5,6,9\}$; Range: $\{-8,-6,3,5,7\}$
B. Domain: $\{-3,1,5,6,3\}$; Range: $\{-8,-6,6,7,9\}$
C. Domain: $\{-3,1,5,6,3\}$; Range: $\{-8,-6,5,7,9\}$
D. Domain: $\{-8,-6,3,5,7\}$ : Range: $\{-3,1,5,6,9\}$
Answer (1)
The domain 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.
Identify the domain: { − 3 , 1 , 5 , 6 , 9 } .
Identify the range: { − 8 , − 6 , 3 , 5 , 7 } .
The correct answer is A: Domain: { − 3 , 1 , 5 , 6 , 9 } ; Range: { − 8 , − 6 , 3 , 5 , 7 } .
Explanation
Finding the Domain The domain of a function represented as a set of ordered pairs is the set of all first elements in the ordered pairs. In this case, the domain is the set of the first elements of the ordered pairs: {6, 9, -3, 1, 5}. We need to write this set in ascending order and without repeating elements.
Finding the Range The range of a function represented as a set of ordered pairs is the set of all second elements in the ordered pairs. In this case, the range is the set of the second elements of the ordered pairs: {-8, 3, 5, -6, 7}. We need to write this set in ascending order and without repeating elements.
Identifying Domain and Range Now, let's identify the domain and range:
Domain: { − 3 , 1 , 5 , 6 , 9 } Range: { − 8 , − 6 , 3 , 5 , 7 }
Selecting the Correct Answer Comparing our calculated domain and range with the given options, we see that option A matches our result.
Option A: Domain: { − 3 , 1 , 5 , 6 , 9 } Range: { − 8 , − 6 , 3 , 5 , 7 }
Examples
Understanding the domain and range of a function is crucial in many real-world applications. For instance, if you're tracking the performance of a stock over a week, the days of the week (Monday, Tuesday, etc.) would be the domain, and the stock prices each day would be the range. Knowing the domain and range helps you analyze the stock's behavior within a specific timeframe and price interval. This concept extends to various fields like weather forecasting (days vs. temperatures), sports analytics (players vs. scores), and even cooking (ingredients vs. dish sizes).
