There are infinitely many possible answers:
etc are all possible rules.
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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 infinitely many possible answers. Rule 1: Add 9 to Input Rule 2: Add 5 to 2*Input Rule 3: Add 1 to 3*Input Rule 4: Subtract -3 from 4*Input or, moving away from whole numbers, Add 3.8 to 2.3 times Input.
There are many functions where if your input is -2 the output is 13. The simplest is probably just adding 15. You could also square -2 (to get 4) and then add 9.
The simplest of infinitely many possible solutions, is y = x2