https://file.aiquickdraw.com/mathbot/file/172996700220659moljf7.jpg

The graph shown is that of the **absolute value function**, represented by:

\[
y = |x|
\]

### Explanation:
1. The absolute value function creates a "V" shape centered at the origin \((0, 0)\).
2. The graph is symmetric with respect to the y-axis, which means for every positive value \(x\), the function returns the same result as for \(-x\).
3. The two arms of the graph have slopes of \(1\) and \(-1\), indicating that:
   - On the right side (when \(x \geq 0\)), the slope is \(1\).
   - On the left side (when \(x < 0\)), the slope is \(-1\).

In general, the absolute value function can be written piecewise as:

\[
y = 
\begin{cases}
x & \text{if } x \geq 0 \\
-x & \text{if } x < 0
\end{cases}
\]

This explains the linear nature of each segment of the "V" shape.

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Do you need further details or have additional questions?

Here are 5 follow-up questions for you:
1. How would the graph change if the function were \(y = |x| + 2\)?
2. What transformation occurs if the function is \(y = |x - 3|\)?
3. How would scaling affect the graph, such as \(y = 2|x|\)?
4. Can you explain the domain and range of the absolute value function?
5. What is the derivative of \(y = |x|\) at \(x = 0\), and why is it undefined?

**Tip:** Absolute value functions are often used to model situations where only positive magnitudes are relevant, such as distances or deviations.

Explore the absolute value function y = |x| with a 'V' shape graph centered at the origin. Learn how the function is defined piecewise and understand the properties of its symmetry and slopes. Ideal for students in Grades 7-9 studying basic algebra and piecewise functions.

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