What kind of transformation converts the graph of f(x)=–2(x–4)2–9 into the graph of g(x)=–2(x–9)2–9?

The transformation that converts the graph of f(x)=–2(x–4)²–9 into the graph of g(x)=–2(x–9)²–9 is a horizontal shift.

Here are the steps to identify the transformation:

1. Compare the two functions. They both have the same form, which is a(x-h)²+k, where a is the coefficient of the squared term, h is the horizontal shift, and k is the vertical shift.

2. In the function f(x)=–2(x–4)²–9, the value of h is 4, which means the graph is shifted 4 units to the right from the origin.

3. In the function g(x)=–2(x–9)²–9, the value of h is 9, which means the graph is shifted 9 units to the right from the origin.

4. The difference in the h values (9-4) is 5, which means the graph of f(x) is shifted 5 units to the right to get the graph of g(x).

So, the transformation from f(x) to g(x) is a horizontal shift of 5 units to the right.