Question
Find the domain and the range of the relation. \( t=\{(9,1),(29,-1),(38,1),(9,9),(51,9)\} \)
Ask by Frank Goodwin. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Domain: {9, 29, 38, 51}
Range: {-1, 1, 9}
Solution
The relation is given by t = {(9,1), (29,-1), (38,1), (9,9), (51,9)}.
Step 1: Find the domain.
The domain consists of all the first elements (inputs) in the ordered pairs:
• 9 (from (9,1))
• 29 (from (29,-1))
• 38 (from (38,1))
• 9 (again, from (9,9)) – already listed
• 51 (from (51,9))
Thus, the domain is {9, 29, 38, 51}.
Step 2: Find the range.
The range consists of all the second elements (outputs) in the ordered pairs:
• 1 (from (9,1))
• -1 (from (29,-1))
• 1 (again, from (38,1)) – already listed
• 9 (from (9,9))
• 9 (again, from (51,9)) – already listed
Thus, the range is {-1, 1, 9}.
Final Answer:
Domain: {9, 29, 38, 51}
Range: {-1, 1, 9}
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The Deep Dive
The domain of the relation \( t \) consists of all the first elements of the ordered pairs. In this case, the domain is \( \{9, 29, 38, 51\} \). The range of the relation includes all the second elements of the ordered pairs. Therefore, the range is \( \{1, -1, 9\} \). So, the domain is \( \{9, 29, 38, 51\} \) and the range is \( \{1, -1, 9\} \).