Question

Describe the transformation that takes f(x) = | x | to g(x) = −|x +4 | − 1

Answer 1

The sign on the 'x' changes, this implies a reflection.

g(x) = -f(x) = -(x+1) = -x -1

Now apply a vertical translation 'up 5' to f(x)

g(x) = -f(x) + 5 = (-x-1) +5 = -x +4

Hope this helps! <3

Answer 2

The negative sign for g(x) flips it. The +4 shifts it the left 4 units and the -1 shifts it down one unit