https://file.aiquickdraw.com/mathbot/file/1726259331341ykyrm2bg.jpg

The graph displayed is a V-shaped function, which is characteristic of an absolute value function. From the graph, we can observe the following:

- The vertex of the graph is at \((0, -1)\), which indicates a vertical shift downward by 1.
- The graph opens downward, suggesting that the absolute value is multiplied by a negative sign.
  
Based on this information, the equation of the graph should be of the form:

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

Thus, the correct equation from the provided options is:

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

This corresponds to the option on the far left: **\( f(x) = -|x| - 1 \)**.

Would you like further details or explanations?

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Here are 5 related questions:
1. How do you determine the vertex of an absolute value function from its graph?
2. What causes an absolute value graph to open downward instead of upward?
3. How does a vertical shift affect the equation of an absolute value function?
4. What is the general form of an absolute value function?
5. How would you describe horizontal shifts in the equation of an absolute value function?

**Tip:** When analyzing absolute value graphs, always check for shifts (horizontal or vertical) and whether the graph opens upward or downward.

Learn how to find the equation of an absolute value graph with a vertex at (0, -1). This problem involves vertical shifts and reflections, typical of algebraic transformations. Suitable for high school students in Grades 9-12.

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