determine the function rule for the following table and predict the next output variable for the blank space

the function rule is there is always 4 more than in the "Out section" than the "In section". The next variable is 18 because 4 more than 14 is 18

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.