https://file.aiquickdraw.com/mathbot/file/1725816486924vbib3rok.jpg

The image contains a set of four graphs representing different functions, along with a task to analyze certain characteristics. Based on the language and the mathematical context, it seems you are being asked to:

1. Identify key features of the functions such as the **domain**, **range**, and **behavior at critical points** (likely extremum, zeros, etc.).
2. Determine intervals where the functions are increasing or decreasing.
3. Analyze the function in terms of continuity or possible asymptotes.

To proceed with solving or analyzing the specific characteristics, I will start by looking at each graph in detail and helping you define their properties:

1. **Graph 1 (Quadratic Parabola)**
   - **Type of function**: Quadratic (parabola) opening downwards.
   - **Domain**: All real numbers.
   - **Range**: Up to the maximum point (vertex).
   - **Behavior**: Decreases to a vertex and then increases symmetrically.

2. **Graph 2 (Absolute Value Function)**
   - **Type of function**: Absolute value function.
   - **Domain**: All real numbers.
   - **Range**: Non-negative values.
   - **Behavior**: Decreasing to 0 and then increasing.

3. **Graph 3 (Piecewise Linear Function)**
   - **Type of function**: Linear segments.
   - **Domain**: Appears to be all real numbers.
   - **

Analyze the characteristics of the functions represented by the graphs, specifically: 1) the function domain; 2) intervals of increase/decrease; 3) behavior at critical points.

This problem focuses on the characteristics of various functions like quadratic, absolute value, and rational functions. Learn to identify the domain, range, intervals of increase and decrease, and critical behavior points with graphical representation. Suitable for high school students (Grades 10-12).

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