Whats the function rule when inputs 2,3,4,5 and outputs 2,5,8,11?
notice that the difference in your inputs in 1, while the difference in your outputs is 3
so you have a slope of 3
let's start with y = 3x + b
when x = 2, y = 2
so
2 = 3(2) + b
-4 = b
f(x) = 3x - 4
check with a few values.
To determine the function rule for the given inputs and outputs, you can look for a pattern in the data provided.
In this case, observe that the outputs increase by 3 as the inputs increase by 1. We can conclude that the function rule involves adding 3 to the input value.
So, the function rule for this specific data set is: f(x) = x + 3.
To check if this function rule is valid, let's apply it to the given inputs:
- For an input of 2, the output should be 2 + 3 = 5, which matches the given output of 5.
- For an input of 3, the output should be 3 + 3 = 6, which does not match the given output of 8.
- For an input of 4, the output should be 4 + 3 = 7, which does not match the given output of 8.
- For an input of 5, the output should be 5 + 3 = 8, which matches the given output of 11.
Since the function rule does not produce the correct outputs for all given inputs, it is not a valid function rule for this data set.