The function $h(x) = |x+6| - 1$ is a transformation of the absolute value parent function $f(x) = |x|$. The transformations applied are:

1. Horizontal Shift: The $+6$ inside the absolute value moves the graph 6 units to the left. This is because the function is of the form $f(x) = |x - h|$, where $h = -6$.

2. Vertical Shift: The $-1$ outside the absolute value moves the graph 1 unit down. This is due to the function being of the form $f(x) = |x| + k$, where $k = -1$.

Summary:

• Horizontal Shift: 6 units to the left.
• Vertical Shift: 1 unit down.

Would you like a detailed graph to visualize these transformations or have any other questions?

Related Questions:

1. What would the transformation be if the function was $h(x) = |x - 4| + 3$?
2. How would the graph of $h(x) = -|x + 6| - 1$ differ from $h(x) = |x+6| - 1$?
3. How do you determine horizontal and vertical shifts in general for any absolute value function?
4. What effect does multiplying $|x + 6|$ by a constant have on the graph?
5. What are some other common transformations that can be applied to the parent function $f(x) = |x|$?

Tip: When analyzing transformations, always start by identifying changes inside and outside the absolute value (or other parent function) separately.