The equation \( y = |x| \) represents a V-shaped graph that opens upwards, with the vertex (or the point of the "V") at the origin \((0, 0)\). Here's how you can visualize the graph:

1. **Shape**: The graph is composed of two straight lines.
   - The line \( y = x \) for \( x \geq 0 \).
   - The line \( y = -x \) for \( x < 0 \).

2. **Vertex**: The point where the two lines meet is called the vertex, and it is located at the origin \((0, 0)\).

3. **Symmetry**: The graph is symmetric with respect to the y-axis, meaning that for every point on the graph at \((x, y)\), there is a corresponding point at \((-x, y)\).

4. **Slope**: 
   - For \( x \geq 0 \), the slope of the line is 1.
   - For \( x < 0 \), the slope of the line is -1.

5. **Range**: The range of the function is all non-negative real numbers, \( y \geq 0 \).

Would you like more details or have any specific questions? Here are some related questions to explore:

1. How does the graph of \( y = |x| \) change if we add a constant, such as \( y = |x| + 2 \)?
2. What happens to the graph of \( y = |x| \) if we introduce a negative sign, like \( y = -|x| \)?
3. How can we describe the graph of \( y = |x - 3| \)?
4. What is the domain and range of the function \( y = |x| \)?
5. How does the graph of \( y = |x| \) compare to \( y = x^2 \)?

**Tip**: Understanding how absolute value functions transform will help you graph more complex functions involving absolute values easily!

Explore the graph of y = |x|, a V-shaped function opening upwards with its vertex at the origin (0, 0). Learn about its shape, symmetry, and range, and understand how to graph transformations involving absolute value functions. Ideal for high school students studying algebra and graphing functions.

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