Identify the following given the relation below.
{(1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}
The relation can be identified as a function.
The given relation is represented as a set of ordered pairs. Each ordered pair consists of two elements: the first element is called the input or x-value, and the second element is called the output or y-value.
Looking at the given relation:
{(1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}
We can identify the following:
1 is paired with 6
2 is paired with 7
3 is paired with 8
4 is paired with 9
5 is paired with 10
Therefore, the input-output pairs in the relation are:
(1, 6)
(2, 7)
(3, 8)
(4, 9)
(5, 10)
The given relation {(1, 6), (2, 7), (3, 8), (4, 9), (5, 10)} consists of pairs of numbers, where the first number in each pair represents the input value and the second number represents the output value.
To identify the pattern or relationship between the input and output values, we can observe the differences between consecutive pairs. Let's calculate the differences using the given relation:
Difference between 2nd and 1st pairs: (2 - 1) = 1
Difference between 3rd and 2nd pairs: (3 - 2) = 1
Difference between 4th and 3rd pairs: (4 - 3) = 1
Difference between 5th and 4th pairs: (5 - 4) = 1
From the observed differences, we can conclude that there is a constant difference of 1 between the input values.
Now, let's observe the differences between the output values:
Difference between 2nd and 1st pairs: (7 - 6) = 1
Difference between 3rd and 2nd pairs: (8 - 7) = 1
Difference between 4th and 3rd pairs: (9 - 8) = 1
Difference between 5th and 4th pairs: (10 - 9) = 1
Again, we can see that there is a constant difference of 1 between the output values.
Based on these observations, we can conclude that the pattern in the given relation is a linear pattern, where the output value is obtained by adding 1 to the input value.
Therefore, the next pair in the pattern would be (6, 11), where 6 is obtained by adding 1 to the previous input value of 5, and 11 is obtained by adding 1 to the previous output value of 10.