Because f(x) has horizontal transformations performed on it to get g(x), it is impossible to fill out the table for g(x) for 2 of the requested x-values. It is possible to know 4 coordinate pairs for g(x), that correspond to the 4 given for f(x). We can find those as follows:
g(x) = 3·f(2(x - 2)) + 3 . Written this way, we see that f(x) is shrunk horizontally by a factor of 2, then shifted 2 to the right. Therefore, the 4 x-values for which the corresponding y-values of g can be found are x = 2, 4, 6, and 8. (These correspond to the x-values 0, 4, 8, and 12 given for f(x). A different, algebraic way to arrive at 2, 4, 6, and 8 is to set 2x - 4 = to 0, 4, 8, and 12 and solve.)
The vertical transformations performed on f(x) are a vertical stretch by a factor of 3, and a shift 3 units up. So, we would multiply f(x)'s values by 3 and add 3 to arrive at the y-coordinates for g: -9 , 3, 33, 39.
x | g(x)
2 | - 9
4 | 3
6 | 33
8 | 39
