Finding rules with Input and output tables


X       Y

1       9

2        12

3         15

4         18


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.