1 2 The graph of the piecewise function f(x) is shown. -4 -3- -7 -6 -5 -4 -3 -2 -1, 3 7 x -2 -3 -6 Mark this ano.retum 寸

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Graph of the Piecewise Function f(x)

#### Description of the Graph:
The graph depicts a piecewise function \( f(x) \) with the following characteristics:

- The graph is plotted on a Cartesian coordinate system with an x-axis range from \(-7\) to \(7\) and a y-axis range from \(-7\) to \(7\).
- There are two distinct linear segments:

  1. **Segment 1 (from \( x = -3 \) to \( x = 2 \))**:
     - Starts at the point \((-3, -1)\) and ends at the point \((2, 4)\).
     - This segment is a continuous line passing through these points.

  2. **Segment 2 (from \( x = 2 \) to \( x = 4 \))**:
     - Begins at the point \((2, 4)\) and ends at the point \((4, 0)\).
     - This segment ends at an open circle at \((4, 0)\), indicating that the value at \( x = 4 \) is not included in the function for this segment.

#### Key Points and Structure:
- The graph begins at \( x = -3 \) and has a continuous straight-line segment passing through the coordinates to reach \( x = 2 \) at \( y = 4 \).
- At \( x = 2 \), the function continues from \( (2, 4) \) but changes the slope leading to an open circle at \( (4, 0) \).

This graph is a visual representation of a piecewise linear function, typically used to showcase functions that have different expressions over different intervals.

The segments and the open/closed nature at specific points illustrate key characteristics of piecewise functions, which are important in understanding behaviors of functions that are defined by multiple sub-functions within different intervals.
Transcribed Image Text:### Graph of the Piecewise Function f(x) #### Description of the Graph: The graph depicts a piecewise function \( f(x) \) with the following characteristics: - The graph is plotted on a Cartesian coordinate system with an x-axis range from \(-7\) to \(7\) and a y-axis range from \(-7\) to \(7\). - There are two distinct linear segments: 1. **Segment 1 (from \( x = -3 \) to \( x = 2 \))**: - Starts at the point \((-3, -1)\) and ends at the point \((2, 4)\). - This segment is a continuous line passing through these points. 2. **Segment 2 (from \( x = 2 \) to \( x = 4 \))**: - Begins at the point \((2, 4)\) and ends at the point \((4, 0)\). - This segment ends at an open circle at \((4, 0)\), indicating that the value at \( x = 4 \) is not included in the function for this segment. #### Key Points and Structure: - The graph begins at \( x = -3 \) and has a continuous straight-line segment passing through the coordinates to reach \( x = 2 \) at \( y = 4 \). - At \( x = 2 \), the function continues from \( (2, 4) \) but changes the slope leading to an open circle at \( (4, 0) \). This graph is a visual representation of a piecewise linear function, typically used to showcase functions that have different expressions over different intervals. The segments and the open/closed nature at specific points illustrate key characteristics of piecewise functions, which are important in understanding behaviors of functions that are defined by multiple sub-functions within different intervals.
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