What is the function rule for input 2 output 6 input 4 output 7 input 6 output 8 input 8 output 9
2--6
4--7
6--8
8--9
difference in the x's is 2, difference in the y's in 1
slope = 1/2
y = (1/2)x + b
use one of the values e.g. (2,6)
6 = (1/2)(2) + b
5 = b
y = (1/2)x + 5
To find the function rule for the given inputs and outputs, we need to analyze the pattern and relationship between the inputs and outputs.
Looking at the inputs and outputs provided:
input 2 --> output 6
input 4 --> output 7
input 6 --> output 8
input 8 --> output 9
To identify the pattern, we can observe how the outputs change as the inputs increase.
From input 2 to input 4, there is an increase of 1 in the output (from 6 to 7).
Similarly, from input 4 to input 6, there is an increase of 1 in the output (from 7 to 8).
And, from input 6 to input 8, there is an increase of 1 in the output (from 8 to 9).
Based on this pattern, we can see that for each increment of 2 in the input, there is an increment of 1 in the output.
Therefore, the function rule can be expressed as: output = (input / 2) + 5.
By substituting different inputs into this rule, we can verify if the outputs match the given data:
For input 2: (2 / 2) + 5 = 6 (matches the given output of 6)
For input 4: (4 / 2) + 5 = 7 (matches the given output of 7)
For input 6: (6 / 2) + 5 = 8 (matches the given output of 8)
For input 8: (8 / 2) + 5 = 9 (matches the given output of 9)
So, the function rule for the given inputs and outputs is output = (input / 2) + 5.