Which ordered pair needs to be removed in order for the mapping to represent a function?
(-3,-4)
(-2,-1)
(1,-3)
(3,7)
Answer (2)
The given ordered pairs are checked for repeated x-values.
It is determined that the mapping is already a function since there are no repeated x-values.
The question is interpreted as requiring the removal of an ordered pair, even though it's unnecessary.
The ordered pair ( − 3 , − 4 ) is arbitrarily chosen for removal, resulting in a function. ( − 3 , − 4 )
Explanation
Understanding Functions The given ordered pairs are ( − 3 , − 4 ) , ( − 2 , − 1 ) , ( 1 , − 3 ) , and ( 3 , 7 ) . A function requires that each x -value maps to a unique y -value. In other words, no x -value can be associated with more than one y -value.
Identifying x-values To determine if the given set of ordered pairs represents a function, we need to check if any x -values are repeated. The x -values in the ordered pairs are − 3 , − 2 , 1 , and 3 .
Checking for Repeated x-values Since each x -value is unique ( − 3 , − 2 , 1 , 3 ), there are no repeated x -values. Therefore, the given set of ordered pairs already represents a function.
Addressing the Question's Premise Since the mapping already represents a function, no ordered pair needs to be removed. However, the question implies that one ordered pair must be removed. Let's assume there was a typo and one of the x values was repeated. If we introduce a new ordered pair, say ( − 3 , 5 ) , then the x value − 3 is repeated. In this case, to make the mapping a function, we would need to remove either ( − 3 , − 4 ) or ( − 3 , 5 ) . Since the original set of ordered pairs is a function, the question is flawed.
Providing an Answer Under Duress Given the original set of ordered pairs: ( − 3 , − 4 ) , ( − 2 , − 1 ) , ( 1 , − 3 ) , and ( 3 , 7 ) , no ordered pair needs to be removed for the mapping to represent a function, as it is already a function. However, if we must remove an ordered pair, any of them would satisfy the condition, albeit trivially. Let's remove ( − 3 , − 4 ) . The remaining ordered pairs are ( − 2 , − 1 ) , ( 1 , − 3 ) , and ( 3 , 7 ) , which still represent a function.
Final Answer Since the question is designed such that one ordered pair must be removed, and the original set already represents a function, removing any of the ordered pairs will result in a function. However, without additional information or constraints, there is no specific ordered pair that needs to be removed. Let's arbitrarily choose to remove ( − 3 , − 4 ) .
Examples
In real life, functions are used to model relationships between different quantities. For example, the relationship between the number of hours worked and the amount of money earned can be represented as a function. If each hour worked corresponds to a unique amount of money earned, then the relationship is a function. Similarly, in computer science, functions are used to map inputs to outputs. Each input must produce a unique output for the function to be well-defined. Understanding functions is crucial in many fields, including mathematics, computer science, and engineering.
The given ordered pairs already represent a function as all x-values are unique, meaning none need to be removed. However, if one must be removed, any can be chosen; for instance, (-3, -4) can be removed, leaving the other pairs still forming a valid function.
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