https://file.aiquickdraw.com/mathbot/file/1725683796795ys9om9bq.jpg

The graph represents a **piecewise linear function**. Specifically, it resembles an **absolute value function** because of the "V" shape. The vertex of the "V" occurs at the point \( (0, 0) \).

To determine the equation, let's consider the following:

1. The function is symmetric about the y-axis, meaning it behaves the same way for positive and negative x-values.
2. The slope of the line on the left side (for negative x-values) is \( -1 \), and for the right side (positive x-values), the slope is \( 1 \).
3. This confirms that the equation is in the form of an absolute value function, with the vertex at the origin \( (0, 0) \).

Thus, the equation for the graph is:

\[
y = |x|
\]

Would you like further details or explanations?

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Here are some related questions:

1. How would the equation change if the vertex was shifted to a different point?
2. Can you explain how the slope affects the appearance of the graph for piecewise functions?
3. What is the significance of the absolute value in this type of function?
4. How would the equation change if the graph were stretched or compressed?
5. What are some other common forms of piecewise functions?

**Tip**: When identifying absolute value functions, always look for the "V" shape and note the location of the vertex for accuracy in the equation.

Complete an equation for the function graphed above.

Learn how to identify and write the equation of an absolute value function from a graph. This problem covers key concepts such as piecewise linear functions and the absolute value equation y = |x|. Suitable for students in Grades 7-10.

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