What kind of transformation converts the graph of f(x)=7|x+4|–1 into the graph of g(x)=7|x–1|+1?

The transformation that converts the graph of f(x)=7|x+4|–1 into the graph of g(x)=7|x–1|+1 is a horizontal shift to the left by 5 units and a vertical shift up by 2 units.

Here's the step-by-step explanation:

1. The function f(x)=7|x+4|–1 is a transformation of the absolute value function, |x|. The "+4" inside the absolute value function shifts the graph 4 units to the left, and the "–1" outside the absolute value function shifts the graph 1 unit down.

2. The function g(x)=7|x–1|+1 is also a transformation of the absolute value function. The "–1" inside the absolute value function shifts the graph 1 unit to the right, and the "+1" outside the absolute value function shifts the graph 1 unit up.

3. To transform f(x) into g(x), we need to shift the graph of f(x) 5 units to the right (from 4 units to the left to 1 unit to the right) and 2 units up (from 1 unit down to 1 unit up).

So, the transformation is a horizontal shift to the right by 5 units and a vertical shift up by 2 units.