The functions f(x) and g(x) are described below: f(x) = 32x + 8 g(x) = 32x − 9 the graph of g(x) is obtained by shifting down the graph of f(x) by units. numerical answers expected!

The given in this item are:
                                f(x) = 32x + 8
                                g(x) = 32x - 9
It can be observed that the expression in the right side of the second function can be obtained by subtracting 17 from the right side expression of the first one. 
                         g(x) = f(x) - 17 = 32x + 8 - 17 = 32x - 9
Thus, the graph is shifted through the vertical axis 17 units down.