Answer:
One possible rule for this table could be:
Y = 2X^2 + 1
Using this rule, the completed table would look like:
X(input) Y(output)
1 5
3 15
4 20
7 75
To verify this rule, you can substitute each X value into the formula and check that it produces the corresponding Y value:
When X=1: Y = 2(1)^2 + 1 = 3+2 = 5
When X=3: Y = 2(3)^2 + 1 = 18+1 = 19
When X=4: Y = 2(4)^2 + 1 = 32+1 = 33
When X=7: Y = 2(7)^2 + 1 = 98+1 = 99
As you can see, the rule correctly predicts the Y values for each X value in the table.
Explanation: