Which of the following sets of ordered pairs represents a function?{(-1,4),(1,4),(2,4),(-2,4)}{(-2,1),(-1,3),(2,1),(-2,2)}{(2,2),(3,3),(4,4),(2,1)}{(-1,3),(-1,4),(-1,5),(-1,6)}
Question
Which of the following sets of ordered pairs represents a function?{(-1,4),(1,4),(2,4),(-2,4)}{(-2,1),(-1,3),(2,1),(-2,2)}{(2,2),(3,3),(4,4),(2,1)}{(-1,3),(-1,4),(-1,5),(-1,6)}
Solution
To determine if a set of ordered pairs represents a function, we need to check if each input (x-value) is associated with exactly one output (y-value). Let's analyze each set of ordered pairs:
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{(-1,4),(1,4),(2,4),(-2,4)}: In this set, all the x-values (-1, 1, 2, -2) are associated with the same y-value (4). Therefore, this set represents a function.
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{(-2,1),(-1,3),(2,1),(-2,2)}: In this set, the x-value -2 is associated with two different y-values (1 and 2). Therefore, this set does not represent a function.
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{(2,2),(3,3),(4,4),(2,1)}: In this set, the x-value 2 is associated with two different y-values (2 and 1). Therefore, this set does not represent a function.
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{(-1,3),(-1,4),(-1,5),(-1,6)}: In this set, the x-value -1 is associated with four different y-values (3, 4, 5, and 6). Therefore, this set does not represent a function.
Based on the analysis, the only set that represents a function is {(-1,4),(1,4),(2,4),(-2,4)}.
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