The function you've written is:

\[
f(x) = |x + 7| - 1
\]

This is an absolute value function. Here's how we can describe it:

### Key Features:
1. **Vertex:** The absolute value function \(|x + 7|\) has a vertex when \(x + 7 = 0\), i.e., when \(x = -7\). So, the vertex of this function is at the point \((-7, -1)\).
   
2. **Shift:** The term \(|x + 7|\) shifts the standard absolute value graph horizontally 7 units to the left (because of \(+7\)).

3. **Vertical Shift:** The \(-1\) outside the absolute value shifts the graph 1 unit downward.

4. **Symmetry:** This function is symmetric with respect to its vertex \(x = -7\).

5. **Range:** Since the absolute value of a number is always non-negative, \(|x + 7| \geq 0\). After subtracting 1, the range of the function is:
   \[
   f(x) \geq -1
   \]
   This means the output will never be less than \(-1\).

### Graphical Behavior:
- For \(x > -7\), the function behaves as \(f(x) = (x + 7) - 1\), which is a line with slope 1.
- For \(x < -7\), the function behaves as \(f(x) = -(x + 7) - 1\), which is a line with slope -1.

Would you like to dive deeper into the graph or other aspects of the function?

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Here are 5 questions that build upon this information:
1. How would the function change if the term \(-1\) were replaced with \(+2\)?
2. What is the domain of this function?
3. How would you solve for \(x\) when \(f(x) = 0\)?
4. What is the significance of the absolute value in functions like this one?
5. How does the slope change across the vertex of this function?

**Tip:** When graphing absolute value functions, always identify the vertex first as it marks the point where the graph changes direction.

Explore the graph of the absolute value function f(x) = |x + 7| - 1. Learn about its key features such as the vertex at (-7, -1), the horizontal and vertical shifts, and how to determine its range and symmetry. This solution is perfect for students in Grades 8-10.

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