Asked by chey
Determine if the set of ordered pairs is a relation or a function.
(0,0),(0,2),(0,3),(0,4)
(0,0),(0,2),(0,3),(0,4)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine if the set of ordered pairs \((0,0),(0,2),(0,3),(0,4)\) is a relation or a function, we need to recall the definitions of these terms.
1. A **relation** is simply a set of ordered pairs. Any set of ordered pairs qualifies as a relation.
2. A **function** is a specific type of relation where each input (the first element of the ordered pair) is associated with exactly one output (the second element of the ordered pair). In other words, no two ordered pairs can have the same first element with different second elements.
In this case, all ordered pairs have the same first element, which is \(0\), but they have different second elements: \(0\), \(2\), \(3\), and \(4\).
Since the input \(0\) is related to multiple outputs (specifically \(0, 2, 3,\) and \(4\)), this set does not meet the criteria to be a function.
Therefore, the set \((0,0),(0,2),(0,3),(0,4)\) is a relation but **not a function**.
1. A **relation** is simply a set of ordered pairs. Any set of ordered pairs qualifies as a relation.
2. A **function** is a specific type of relation where each input (the first element of the ordered pair) is associated with exactly one output (the second element of the ordered pair). In other words, no two ordered pairs can have the same first element with different second elements.
In this case, all ordered pairs have the same first element, which is \(0\), but they have different second elements: \(0\), \(2\), \(3\), and \(4\).
Since the input \(0\) is related to multiple outputs (specifically \(0, 2, 3,\) and \(4\)), this set does not meet the criteria to be a function.
Therefore, the set \((0,0),(0,2),(0,3),(0,4)\) is a relation but **not a function**.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.