Answer:
Horizontal translation → Reflection about x-axis → Vertical Translation
Step-by-step explanation:
We are given the function f(x) = |x|.
This function is transformed to the new function given by g(x) = - |x+4| - 1.
So, we see that,
1. Translation of 4 units to the left is applied, which changes f(x) = |x| to |x+4|.
2. Reflection about x-axis is applied, which changes |x+4| to - |x+4|.
3. Finally, translation of 1 unit downward is applied, which changes - |x+4| to g(x) = - |x+4| -1.
Hence, the sequence of transformation applied to obtain g(x) from f(x) is Horizontal translation → Reflection about x-axis → Vertical Translation.
