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.