Which of the following relations are functions?R1 ={(3, 4),(4, 5),(6, 7),(8, 9)}, R2 ={(3, 4),(4, 5),(6, 7),(3, 9)}, R3 ={(-3, 4),(4, -5),(0, 0),(8, 9)}, R4 ={(8, 11),(34, 5),(6, 17),(8, 19)}
Question
Which of the following relations are functions?R1 ={(3, 4),(4, 5),(6, 7),(8, 9)}, R2 ={(3, 4),(4, 5),(6, 7),(3, 9)}, R3 ={(-3, 4),(4, -5),(0, 0),(8, 9)}, R4 ={(8, 11),(34, 5),(6, 17),(8, 19)}
Solution
A function is a relation in which each input has exactly one output. In other words, a relation is a function if no two pairs in the relation have the same first element.
Let's check each relation:
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R1 ={(3, 4),(4, 5),(6, 7),(8, 9)}: In this relation, each input (the first number in each pair) is unique. Therefore, R1 is a function.
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R2 ={(3, 4),(4, 5),(6, 7),(3, 9)}: In this relation, the input 3 is associated with two different outputs (4 and 9). Therefore, R2 is not a function.
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R3 ={(-3, 4),(4, -5),(0, 0),(8, 9)}: In this relation, each input is unique. Therefore, R3 is a function.
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R4 ={(8, 11),(34, 5),(6, 17),(8, 19)}: In this relation, the input 8 is associated with two different outputs (11 and 19). Therefore, R4 is not a function.
So, the relations R1 and R3 are functions, while R2 and R4 are not.
Similar Questions
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