What kind of transformation converts the graph of f(x) = -9|x + 1| + 1 into the graph of g(x) = -9|x – 7|?

To determine the transformation from ( f(x) = -9|x + 1| + 1 ) to ( g(x) = -9|x – 7| ), we can analyze the changes in the equation:

1. The function ( f(x) ) has a vertex at ( (-1, 1) ).
2. The function ( g(x) ) has a vertex at ( (7, 0) ).

To find the transformation, we can observe that:

– The horizontal shift is from ( -1 ) to ( 7 ): this is a shift to the right by ( 8 ) units.

– The vertical shift from ( 1 ) to ( 0 ) indicates a downward shift by ( 1 ) unit.

So, the transformation is a translation 8 units right and 1 unit down.

Therefore, the correct answer is:

translation 8 units right and 1 unit down.