What kind of transformation converts the graph of f(x)=5|x–7|–9 into the graph of g(x)=5|x–3|?

The transformation that converts the graph of f(x)=5|x–7|–9 into the graph of g(x)=5|x–3| is a horizontal shift to the right by 4 units.

Here's the step-by-step explanation:

1. The function f(x)=5|x–7|–9 is an absolute value function. The graph of this function is a V-shaped graph that opens upwards. The vertex of this graph is at (7, -9).

2. The function g(x)=5|x–3| is also an absolute value function. The graph of this function is also a V-shaped graph that opens upwards. The vertex of this graph is at (3, 0).

3. Comparing the two functions, we can see that the only difference is in the value inside the absolute value function. In f(x), it's |x-7|, while in g(x), it's |x-3|.

4. This means that the graph of f(x) has been shifted to the right by 4 units to get the graph of g(x). This is because the value inside the absolute value function determines the x-coordinate of the vertex of the graph.

So, the transformation is a horizontal shift to the right by 4 units.