We conclude that the following relations are the functions.
{(1, 3), (2, 4), (3, 5), (4, 6), (5, 7)}{(3, 1), (4, 1), (5, 1), (6, 1), (7, 1)}{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}
Step-by-step explanation:
1)
Given the first relation
{(1, 3), (2, 4), (3, 5), (4, 6), (5, 7)}
We know that a function tends to relate input to an output.
A function relates an input to an output, where each input is related to exactly one output.
In the given relation, each input is related to exactly one output. In other words, there is no repetition of the x value, meaning the input is unique.
Therefore, the given relation is a function.
2)
Given the first relation
{(3, 1), (4, 1), (5, 1), (6, 1), (7, 1)}
In the given relation, each input is related to exactly one output. In other words, there is no repetition of the x value, meaning the input is unique.
Therefore, the given relation is a function.
3)
Given the first relation
{(-5, 4), (-3, 2), (-1, 0), (-3, -2), (-5, -4)}
In the given relation, there is a repetition of x elements.
i.e. -5 is repeated twice.
It means the input is not unique.
Therefore, the given relation is not a function.
4)
Given the first relation
{(1, 0), (1, 2), (3, 2), (5, 4), (7, 6)}
In the given relation, there is a repetition of x elements.
i.e. 1 is repeated twice.
It means the input is not unique.
Therefore, the given relation is not a function.
5)
Given the first relation
{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}
In the given relation, each input is related to exactly one output. In other words, there is no repetition of the x value, meaning the input is unique.
Therefore, the given relation is a function.
Therefore, we conclude that the following relations are the functions.
{(1, 3), (2, 4), (3, 5), (4, 6), (5, 7)}{(3, 1), (4, 1), (5, 1), (6, 1), (7, 1)}{(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}
