To complete the table for the linear function y = 3x, we need to substitute each value of x into the equation and calculate the corresponding value of y.
x y
-2 -6
-1 -3
0 0
1 3
2 6
3 9
To find the values of a, b, and C, we can look for a pattern in the input-output table.
The value of a is the y-intercept of the function, which is the value of y when x = 0. From the table, we can see that y = 0 when x = 0, so a = 0.
The value of b is the slope of the function, which is the change in y over the change in x. From the table, we can see that the change in y is 3 when the change in x is 1, so b = 3.
The value of C is the output when x = -3. From the table, we can see that y = -9 when x = -3, so C = -9.
Therefore, the completed table and values of a, b, and C are:
x y
-2 -6
-1 -3
0 0
1 3
2 6
3 9
a = 0
b = 3
C = -9