The relation {(-1 , 3), (4 , 2), (-1 , 5)} is not a function ⇒ 2nd
Step-by-step explanation:
Let us revise the meaning of relation and function
- The relation is a set of inputs and outputs
- A function is a relation with one output for each input, that means every x has only one y
- Ex: {(2 , 3) , (-1 , -2) , (3 , 2)} is a function because 2 has only 3 , -1 has only -2 and 3 has only 2, {(1 , 7) , (2 , -4) , (1 , -3)} is not a function because 1 has 7 and -3
The relation is a function if and only if every x has only one y
In {(0 , 0), (1 , 0), (2 , 0)}
∵ x = 0 has y = 0
∵ x = 1 has y = 0
∵ x = 2 has y = 0
∴ Every x has only one y
∴ {(0 , 0), (1 , 0), (2 , 0)} is a function
In {(-1 , 3), (4 , 2), (-1 , 5)}
∵ x = -1 has y = 3
∵ x = 4 has y = 2
∵ x = -1 has y = 5
∴ x = -1 has y = 3 and 5
∴ Not every x has only one y
∴ {(-1 , 3), (4 , 2), (-1 , 5)} is not a function
In {(1 , 2), (3 , -5), (-1 , 7)}
∵ x = 1 has y = 2
∵ x = 3 has y = -5
∵ x = -1 has y = 7
∴ Every x has only one y
∴ {(1 , 2), (3 , -5), (-1 , 7)} is a function
In {(7 , -1), (3 , -2), (5 , -2)}
∵ x = 7 has y = -1
∵ x = 3 has y = -2
∵ x = 5 has y = -2
∴ Every x has only one y
∴ {(7 , -1), (3 , -2), (5 , -2)} is a function
The relation {(-1 , 3), (4 , 2), (-1 , 5)} is not a function
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You can learn more about the relations and functions in brainly.com/question/10570041
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