To create an absolute value function that represents the lower function on the graph, we need to analyze the form of absolute value equations, which generally look like \( y = a |x - h| + k \), where \( (h, k) \) is the vertex of the V-shape, and \( a \) determines the direction and steepness of the V.
To determine the proper equation, we need to identify the vertex of the lower function from the graph and see how it aligns with the values on the axes.
Here are the steps you should take to derive the equation:
- Identify the vertex: Check the lowest point of the V. Note the coordinates (h, k).
- Determine the slope: Examine how the lines extend from the vertex to find the slope which denotes 'a'.
- Write the equation: Plug in the vertex coordinates into the general form.
Suppose the identified vertex from the graph is at (-2, 4) and slopes down with a rise/run ratio giving a steepness that suggests \( a = -1 \). Then the equation could be modeled as:
\[ y = -1 |x + 2| + 4 \]
or simplified to:
\[ y = -|x + 2| + 4 \]
This model indicates that the shape opens downward with the vertex located at (-2, 4).
Without the specific details of the angles and slopes from the graph, please adjust as needed based on the vertex and slopes you observe on the actual graph.
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