the function h(x)=|x+6|-1 performs what transformations on the absolute value parent function?

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.

The function h(x) = |x+6| -1 performs what transformations on the absolute value parent function?

Discover how the function h(x) = |x + 6| - 1 transforms the absolute value parent function. This solution explains the horizontal shift 6 units left and the vertical shift 1 unit down. Learn about transformations of absolute value functions, suitable for students in Grades 8-10.

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