Finding rules with Input and output tables
To find a rule for this table you have to look at what the Y (output) side goes up by so in this example it goes up by 3 every time.
the second step is to multiply X (the input number) by the number that y goes up by
2×3 which equals 6
but if you look at the graph the output number for 2 should be 12 so to get from 6 to 12 you would need to add 6
so the rule would be Y=X3 + 6
you can test to see if this is correct by trying it with the other input numbers and seeing if you get the same output numbers as the chart.