https://file.aiquickdraw.com/mathbot/file/1727889543029avg9gf7o.jpg

The graph you've shared shows a V-shaped graph, which is a characteristic of an absolute value function. The vertex of the graph is at the point (-4, 0), indicating a horizontal shift of 4 units to the left from the origin.

Among the given options, let's analyze each one:

1. **\( y = |x| + 4 \)**: This represents a standard absolute value function shifted 4 units up. This does not match the graph because the graph is not shifted upward.

2. **\( y = |x + 4| \)**: This is an absolute value function shifted 4 units to the left, which fits the graph's vertex at (-4, 0). This seems to be the correct equation.

3. **\( y = |x| - 4 \)**: This would shift the graph 4 units down, which does not match.

4. **\( y = |x - 4| \)**: This would shift the graph 4 units to the right, but the vertex is at (-4, 0), so this is not correct.

Thus, the correct equation that matches the graph is:
\[
y = |x + 4|
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. How would the graph change if the equation were \( y = |x - 3| \)?
2. What happens to the graph of \( y = |x + 4| \) if you add a constant inside the absolute value?
3. How do you determine the vertex of the function \( y = |x + a| \)?
4. What transformation does the function \( y = -|x| \) represent?
5. How can you graph the function \( y = |x + 2| - 3 \)?

**Tip:** The expression inside the absolute value, \( x + c \), controls horizontal shifts, while constants outside control vertical shifts!

Identify the correct equation for an absolute value graph with a horizontal shift. This problem covers key algebra concepts, including graphing absolute value functions and transformations. Suitable for students in Grades 7-9.

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