The relationship between the input and output values is typically defined by a function. In this case, if the input is 6 and the output is 4, the function could be represented as f(x) = x - 2. This function subtracts 2 from the input value to get the output value.
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There are infinitely many possible answers:
Rule I: Output = 4 (whatever the input, the output is 4).
Rule 2: Output = Input - 2
Rule 3: Output = Input/2 + 1
Rule 4: Output = (Input/3)2
There are an infinite possible answer. Among the simpler ones is: Output = Input - 2
The rule appears to be a linear relationship between the input and output values. When the input increases by 4 (from 1 to 5), the output decreases by 4 (from 5 to 1). Similarly, when the input increases by another 4 (from 5 to 9), the output decreases by 4 again (from 1 to -3). Therefore, the rule seems to be that for every increase of 4 in the input, the output decreases by 4.
The rule used in this input-output relationship appears to be dividing the input numbers by 3 to get the corresponding output numbers. This can be deduced by observing that 3 divided by 3 is 1, 15 divided by 3 is 5, 18 divided by 3 is 6, and 27 divided by 3 is 9. Therefore, the rule is to divide the input numbers by 3 to obtain the output numbers.
There are many rules for that pair. Without further information about the kind of operators expected to be used it is impossible to give an answer. Let me give you a very simple example: What is the rule for input 2 output 4: rule 1: x → x + 2 rule 2: x → 2x rule 3: x → x^2 rule 4: x → x^3 ÷ 2 rule 5: x → x^3 - x^2 rule 6: x → x^3 - 2x rule 7: x → x^3 - 4 rule 6: x → x^4 - x^3 - x^2 etc Even with a list of permissible operators, there is no one definite answer given only one pair of input/output - it would require further examples of inputs and their corresponding outputs to be able to narow the possible answers: only slightly as it is still possible to find [infinitely] many polynomials that provide the given input/output pairs.
if one answer is 6 and the other answer is 7, how do the output numbers from the input/output machines compare