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To define the piecewise function based on the graph you provided, we need to break the function into intervals according to changes in the behavior of the graph. Here's an analysis of the graph:

1. **Interval 1: \( x \leq -2 \)**  
   The graph follows a downward curved shape, indicating a quadratic form. The point given is \((-2, 4)\). We assume the function is quadratic before \(-2\), likely of the form \( y = ax^2 + bx + c \). We will need more points or additional assumptions to derive the exact equation here.

2. **Interval 2: \( -2 < x \leq 0 \)**  
   This segment is a straight line from \((-2, 4)\) to \((0, 0)\). The slope of this line is:
   \[
   m = \frac{0 - 4}{0 - (-2)} = \frac{-4}{2} = -2
   \]
   The equation of the line can be written as \( y = -2x + 0 \), so for this interval:
   \[
   y = -2x
   \]

3. **Interval 3: \( 0 < x \leq 4 \)**  
   In this section, the graph is a horizontal line from \((0, 0)\) to \((4, 1)\), indicating a constant function. The equation is:
   \[
   y = 1
   \]

4. **Interval 4: \( 4 < x

Learn how to define a piecewise function from a graph with intervals showing linear and quadratic equations. This problem involves analyzing changes in graph behavior to form equations for each segment. Suitable for students in Grades 9-12.

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