https://r2.erweima.ai/mathbot/image/1726770285737f4j8q39e.jpg

The graph shown represents a **V-shaped** graph, which indicates it is the graph of an **absolute value function**. The graph has two linear sections, with the vertex located at the origin \((0, 0)\).

### Key observations:
1. The function has a vertex at \((0, 0)\), meaning the equation should not have any horizontal or vertical shifts.
2. The slope of the left branch (negative x-values) is \(-1\), and the slope of the right branch (positive x-values) is \(1\).
3. These slopes match the typical shape of the absolute value function \(y = |x|\), which has two linear parts with slopes \(\pm 1\).

Thus, the equation represented by the graph is:
\[
f(x) = |x|
\]

Would you like further details or have any questions?

Here are five related questions for further exploration:
1. What would happen to the graph if we added a constant to the function \(f(x) = |x|\)?
2. How would the graph change if the vertex of the absolute value function were shifted to \((2, 3)\)?
3. How can we describe the domain and range of the function \(f(x) = |x|\)?
4. What is the effect of multiplying the absolute value function by a negative constant?
5. How can we use the vertex form of an absolute value function to model real-world situations?

**Tip:** The absolute value function is defined as \(f(x) = |x| = \begin{cases} 
x, & \text{if } x \geq 0 \\
-x, & \text{if } x < 0
\end{cases}\), which gives it its characteristic V-shape.

A graph of a function is shown. Which of the following equations is represented by the graph?

Analyze the graph of an absolute value function to identify its equation. The V-shaped graph represents the function y = |x|, showing how absolute values create two linear sections with slopes of +1 and -1. Suitable for students in Grades 8-10.

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